6. Find the general solution of 2x(3x + y – ye-**)dx + (x² + 3y2 + e-**)dy = 0

Q: 4. Find the particular solution of y(x² + y²)dx + x(3x² – 5y²)dy ;where x = 2 and y = 1. -

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Q: 1. Determine the general solution of (x + 3y)dx - x dy = 0

A: Here in 1. we have to find general solution of given differential equation,        As per our…

Q: 4. General solutions of differential equations (x² + y² +x)dx + xy dy = 0 is..

A:

Q: 2 What is the solution of the initial – value problem d²y =X O with y(0) = 1 dx? and y'(0) = -2 ? у…

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Q: 3) Find the solution of Initial Value Problem dy 2x-sin y dx 2x cos y ; y(4)=0

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Q: 3. Solve the initial-value problem: 2 dy = 2xy + 3y y(1) = dx 1

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Q: 10.Obtain the general solution of y(8x – 9y)dx + 2x(x – 3y)dy = 0

A: First we find tha integrating factor of given differential eq then we get exact differential eq.So,…

Q: Example 2: Find the particular solution of (x – y)dx + (3x+y)dy = 0 when x = 2 & y = -1.

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Q: If we use the method of variation of parameters, the particular solution of the following…

A: We have to assume the proper solution first.

Q: 2. Solve the differential equation (3x2 – x³ + 3y – 3.ry – y°)d.x + 3(x + y²)dy= 0, - -

A: Disclaimer: Since, you have requested for a handwritten solution and currently we are not providing…

Q: If we use the method of variation of parameters, the particular solution of the following…

A: 2y''-4y' =2xGeneral solution :2D2-4D = 0D(2D-4)=0 D = 0 2D-4 = 0 D=2 GENERAL SOLUTION :Y = C1e2X+C2

Q: Problem 2.3 i. and 2.3 ii

A: Given initial problems are

Q: 4. Solve (D-1)y (x'+2x +x+6)e using differential operators method.

A: Consider a homogenous differential equation: ay''+by'+cy=0 Write an auxiliary equation corresponding…

Q: (2) The particular solution y,(x) to the differential equation y" + 100y = sec2 (10x) is of the %3D…

A: Given y"+100y=Sec2(10x) ---1Compairing with y"+q(x)y'+r(x)y=g(x).Auxilliary equation corresponding…

Q: 3. Get the general solution of the differential equation (x+2y-4)dx- (2x+y-5)dy%3D0.

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Q: Verify that y=2 cos(3x) is a solution to the initial value problem: y"+9y=0, y(0)= 2

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Q: Solve the initial value problem. 2x* - х - 4 2 dy X dx (x+1)(у+1) y(1) = 3

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Q: 2. Give the general solution of xy'dy = (x³ +y³)dx in explicit form.

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Q: 2. Find the general solution of (2x-3y-2) dx-(x-2y)dy = 0

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Q: (6) Show that the solution of the differential equation dr 3 + dy 3(y + 1) is r (y + 1)³ + c y +1 y…

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Q: 2. Find the general solution of d²y dy +5- dr.² dx 6y=0

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Q: What is the particular solution to the differential equation dy/dx=xy2 with initial condition y(2) =…

A: To find the particular solution

Q: 4. Solve (D² -1)y =(x'+2x² + x +6)e²* using differential operators method.

A: Let us consider differential equation: ay''+by'+cy=f(x) Write auxiliary equation to get…

Q: Find an explicit solution of the given initial-value problem. √₁-y² dx - √1-x² dy = 0, y(0) = -1/ 1-…

A: The given differential equation,1-y2dx-1-x2dy=0, y0=12

Q: Solve the differential equation (y+xy+ 1) dx + (x²+xy²+2y) dy=0 by forming integrable combinations.

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Q: Solve the initial value problem (x² + 4)- dy + 3xy = x, y(0) = 1. dx

A: Given the differential equation,  (x2+4)dydx+ 3xy = x , y(0) = 1 (x2+4)dydx+ 3xy=x(x2+4)dydx=x -…

Q: Suppose dr - =4sin(2x) and y= -2 when *=. what is the particular solution to the given differential…

A: In this question, we need to find the particular solution to the given differential equation.

Q: 4. Solve (D -1)y =(x +2x* +x+6)e" using differential operators method.

A:

Q: 3. Find an explicit solution of the given initial-value problem. dy y² sin x, y( 2) - dx

A: We Solve Given IVP by Variable Separable Form of Differential equations.

Q: what is the solution to the differential equation 2\sqrt(xy)(dy)/(dx)= 1 at y(4)=1

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Q: How do I solve dx/dt+2x=3 with a particular solution of xp=3/2?

A: To find the general solution of the equation, given the particular solution

Q: In the differential equation (2x+3y-5)dx+(3x- y-2)dy=0, the lines 2x+3y-5 =0 and 3x- y-2 =0…

A: This question can be solved using the concept of solving two linear equation.

Q: Express the solutions of the initial value problems in terms of integrals. dy dx = √(1 + x2), y(1) =…

A: Consider the given equation as dx=1+x2dy

Q: -dt solves the initial value problem 35. Show that y = x² + d² y 2 x²* 3; y'(1) = 3, y(1) = 1. dx…

A: Given

Q: Solve the initial value problem dx 2x = cos(4t) dt with x(0) = 1. x(t) = sqrt(-1/4sin(4t)+1)

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Q: 5. Find the General and Particular solution of 2 = 3y ; y = 3, when x = 0 dy dx

A: We have dydx=3y Now, we can write this as: dyy=3dx Now, integrate both sides: ∫dyy=∫3dx⇒lny=3x+C…

Q: Find the particular solution of the given differential equations. 2. (x² + 2xy - 4y²)dx - (x² - 8xy…

A: (x² + 2xy - 4y²)dx - (x² - 8xy - 4y²)dy = 0

Q: Solve this homogenous differential equation (separable of variables) problem:…

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Q: Solve the initial value problems 1.dy/dx = 2x - 7, y(2) = 0    2. dy/dx = 10 - x, y(0) = -1

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Q: The differential equation 3y(x -1dx+(x³ +8y– 3xdy = 0; is exact because OM ON %3D

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Q: How do I solve this non-exact DE (4x+3y-7) dx+ (4x + 3y+1) dy=0?

A: Consider the substitution, z = 4x + 3y

Q: 3 9 dx dt -1 -3 with x(0) 4 Give your solution in real form. X1 = X2 = ||

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Q: 4. Solve (D-1)y=(x'+2x+x+6)e using differential operators method.

A: Given: D2-1y=x3+2x2+x+6e2x

Q: Find an explicit solution of the given initial-value problem. 2 dy dx = y - xy, y(-1) = -3 y =

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Q: Find general solutions of bernoulli differential equations.   y' + 2xy = -xy^4

A: The given Bernoulli differential equation is,

Q: 2. Give the general solution of xy dy = (x³ + y³)dx in explicit form.

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Q: 4. Test the existence and uniqueness of solutions of the initial value problem: dy 2xy y(-1) = 1 dx…

A: The given differential equation is dydx=2xy4+x2+y2.      y(-1)=1. To Check: Existence and uniqueness…

Q: 4. Find the general solution of (x + y³) dx = 3xy² dy

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Q: 2. Obtain the general solution of: xy dx – (x² + 3y²) dy = 0

A: