2. What should be A for the exact differential equation of 2.Ay – x y? ry + A , + IP¬ Moreover evaluate the exact differential equation for this value | -dy of A.

Q: Show that the differential equation x²y³ + x(1+y²)y' = 0 is not exact, but becomes exact when…

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Q: Consider the differential equation: 2 9y"y" – 6(y')² = y" When making the change of variable v =…

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Q: 8. consider the differential equation x*y3 + x(1 + y²) = 0 Which of the following integration factor…

A: Integrating factor is not unique. So check the correct option by multiplying the given differential…

Q: 5 Find the general solution of the differential equation: (1+x³ ) dy – x² y dx = 0 %3D Then find the…

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Q: Given that y = 3e is a solution of the differential equation %3D y" + 3y' = 0. Then, by using…

A: Follow next step

Q: he particular solution to the differential equation dy/dx= xy+y, given y=e when x=0, is of the form…

A: Given : The differential equation  is dydx=xy+y with y=e when x=0.  the particular solution for the…

Q: [2] Determine the values of r for which the differential equation 2y"+ 5y'- 3y = 0 has solutions of…

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Q: 2.2 Find the solution of the differential equation d'x dx + + 3z + 8x dt dz %3D dt? dt

A: Given: d2xdt2+dxdt+8x=dzdt+3z

Q: Consider the following differential equation. 2y'' + y' − y = 0 Exercise (a) For what values of…

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Q: 1. The general solution to the differential equation below is: + csc(y) = 0 %3D O In(csc(y) –…

A: According to our guidelines , we can answer only first question. Kindly re-post other remaining…

Q: a) Is a unique solution guaranteed for the differential equation below? Do not solve the DE. Support…

A: note : as per our guidelines we are supposed to answer only one question. Kindly repost other…

Q: 1 Obtain the particular solution for the following differential equation if y(n) = 1 (3x? + ycosx)dx…

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Q: 5. Obtain the particular solution for the given differential equation when SHOW YOUR COMPLETE AND…

A: topic- differential equations

Q: Evaluate the given differential equation (2x + 3)y' = y + (2x + 3)2 a. y = In(2x + 3) +C b.y = (2x +…

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Q: What is the general solution of of the differential equation y = ysecz ? O (sec z+ tan z) - c O y…

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Q: 4. (а) Find the general (implicit) solution to this differential equation. dy x – 5 (x – 1) dx y²(x…

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Q: 2. Consider the following first order ordinary differential equation (x+ y) dy – (x – y) dx = 0 Show…

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Q: Determine the values of r for which the differential equation 2y"+ 5y'- 3y = 0 has solutions of the…

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Q: Find the general solution of the given second-order differential equation. y" – 6y' + 10y = 0 %3D…

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Q: Show that xy = ae" +be* +x is a solution of the differential equation. d'y +2- -x+x-2=0. X dx

A: If we differentiate   the given  solution equation two times  and  get  the given differential…

Q: 2. (a) Check that the first order differential equation 3x dy - 3y = 10(/xy* ) is homogeneous and…

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Q: Given: 1+ ce y = 1- ce 1+ ce y = 1- ce is a solution to the differential equation Show that dy 1 (ỷ…

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Q: 3. (2xy? – y)dx + (x + 3y*)dy = 0 Ans: y(y3 + x2 + c) = x

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Q: Determine the values of r for which the differential equation y' + 3y = 0 has solutions of the form…

A: The given differential equation is,y'+3y=0

Q: 4. (2x? + y)dx + (x²y – x)dy = 0 Ans: 4x2 – 2y + xy² = cx %3D

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Q: What is the integrating factor of the given differential equation? 3 3 (2y – xHdx + 3x²ýdy = 0 А. у?…

A: GIVEN: (2y3 - x3) dx + 3x2y dy = 0

Q: Let y be a solution of the differential equation y' + !y = -2a°y^, where a > 0, y > 0 such that y(1)…

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Q: What is the value of y(0) if y(t) is a solution of the differential equation? 1 y' (t) + 2y(t) = 1…

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Q: (b) Consider the differential equation ydr+r(lnx-lny - 1)dy = 0. (i) Show that the equation is a…

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Q: 1. Solve the differential equation for y= y(t) given the initial condition. dy 1 dt ty – y with y(2)…

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Q: How does the following differential equation y dr + x dy = 0 satisfy the criterion for an exact…

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Q: Given, (1/x^2+1/y^5)dx+(Ax+1/y^6)dy=0 is an exact differential equation. Determine the value of A.

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Q: 1. Use suitable substitution to solve the following differential equations: dy (a) dr : = (x + y +…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: 3) Consider the differential equation (5y³ – 5x)dx – 15xy?dy = 0 In order for the expression 5y3 =…

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Q: What is the general solution for the following differential equation? d²y dr² dy 4+y=0 dr…

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Q: 1 y2 t2 – 1

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Q: What form of the particular solution is appropriate for the differential equationy "'- y'=4? A B C D…

A: To determine the form of the particular solution that is appropriate for the differential equation…

Q: Show that the differential equation x¹y5 + x(1+y¹)y' = 0 is not exact, but becomes exact when…

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Q: dy dr What condition does a differential equation in the form M(x, y) + N (x, y) = 0 need to satisfy…

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Q: Show that the differential equation xy + x(1+y¹)y=0 is not exact, but becomes exact when multiplied…

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Q: 2. Consider the following first order ordinary differential equation (x + y) dy – (x – y) dx = 0…

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Q: Solve for the value of "C" on the given differential equation below. Let y( 0 )=1 2( 2xy +4y -3 )dx…

A: We have to solve given differential equation:

Q: 1. Let the following higher order differential equation (1) y" - 2 y" – 3y = 3 e. Determine the…

A: NOTE: Hi! Thank you for your question. As per the honor code, we'll answer the first question since…

Q: Find the general solution of the given second-order differential equation. 3y" + 2y' + y = 0 y(x) =…

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Q: 3. Given the DE with the form y' + yP(x) = (y^n)Q(x), where n is any real number. If n = 1, the…

A: I have show that for , n=1 given differential equation becomes variable seperable differential…

Q: What is the general solution to the differential equation y- (9 - + = 0 ? dx In(Ay – 2) = Ax +B y2 =…

A: We have given a differential equation ,  yd2ydx2 - dydx2 + dydx = 0 This can be written as ,  y y''…

Q: Let F(x) be the particular solution of the e2x differential equation Y"-2y +y = (e* + 1)? * What is…

A: This is a problem of Non-homogeneous differential equation. In which we have to find particular…

Q: Prove or disprove that the function y = t exp is a solution to the differential equation y = y" +…

A: Given differential equation is y=y''+y' ⇒y''+y'−y=0 Write the auxiliary equation m2+m−1=0…

Q: 2. Verify that the indicated expression is a solution for the given differential Equation dy x3y3 –…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.