g(x) = t² - t dt g'(4)

Q: (x² + y²)dx – xydy = 0 -

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Q: Find the particular solution for initial value problem.

A: x2dydx-yx=0⇒x2dydx=yx⇒dyy=xx2 dx⇒dyy=x12·x-2 dx⇒dyy=x-32 dx Now integrating on both sides, we get…

Q: Determine the quadrants in which the solution of the differential equation dy/dx = (1/2)xy is an…

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Q: The separable equation dy/dx=xy2 admits a constant solution equal to (x)=0. Is it True or False?

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Q: I Solve the differential equatons when X= (x+y) dx +(2xy+xh 3x) dy=o 1. Y= 2

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Q: Given: D^2y-y=x Using Variation of parameters, what is the complete soln of the  differential…

A: This question is based on solution of differential equation using variation of parameters.

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).

A: Given: f'(x)=6x f(0)=8 Integrate the equation. ∫f'(x)=∫6xf(x)=6x22+Cf(x)=3x2+C

Q: Find the general solution of the differential equation dx =t (1+t² ) sec² x dt.

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).

A: Explanation: Given that,  f''(x)=sinxf'(0)=1f(0)=6       Concept Used:

Q: Solve the initial value problem dy/dx=x^2+1/x^2, y=-1 when x=1.

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Q: Solve the initial-value problem. dy for x21 with y(4) = 4 %3D dx The solution to the initial-value…

A: We have to solve the initial-value problem: dydx=5x Solving by variable separable method,…

Q: Solve the initial value problem. dx 3. t2 + 3tx = t* In t + 1, x(1) = 0 dt

A: To solve the initial value problem.t2dxdt+3tx=t4 ln t+1,     x1=0

Q: Solve for the particular solution of the following differential equUations. a. (x³ + 3y)dx –- xdy;…

A: The given differential equation is: x3+3ydx-x dy=0 ;    y(1)=3

Q: Show if the the initial value problem is dy separable or not -=y²(1+x²) • dx vith the initial value…

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Q: Solve the initial value problem. √y dx + (x-4)dy=0, y(5)= 36

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Q: SOLVE THE FOLLOWING HOMOGENOUS LINEAR DIFFERENTIAL EQ TACHY 1. (D³ - 5D² + 3D + 9)y = 0 2 (D3 D2 1

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Q: 5. Verify that y(x) = Vx+C is a solution of the differential dy dx 1 for every constant C. equation…

A: The differential equation is given as dydx=12y2ydy=1dx

Q: dy/dx= 2ex-e-x y(0)=5

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Q: Solve the initial value problem given below. dy – 16xy and y = -2 when x = -4 %3D | dx

A: Given: dydx=-16xy, and y=-2 when x=-4 i.e. y-4=-2. To Solve: The given initial value problem.

Q: dy (sec x) dx eуtsin x

A: Given : The differential equation sec xdydx = ey + sin x

Q: Find the function which solves the initial value problem dy/dx=2x−2, y(2)=−7 y(x)=?

A: The solution is:

Q: Solve the initial value problem dy/dx=2x−1x2, x≠0, y(1)=5.

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Q: Solve the given initial value problem for y=f(x) 1) dy/dx=3x-2 where y=2 when x=-1

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Q: Verify that the function y = Ce5x is a solution of the differential equation           y′ = 5y

A: The given function is  y = Ce5x  The differential equation is y′ = 5y

Q: After separating the variables, the differential equation takes the form 2x gly) dy= 0. Compute f(-…

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Q: Solve the initial value problem √y dx + (x - 2)dy = 0, y(3) = 9

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Q: Find the particular solution of the differential equation that satisfies the initial condition. 1 dy…

A: The given differential equation is: dydx=14-x2 ;                 y(0)=π

Q: Find the general solution of the differential equation and check the result by differentiation.…

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Q: Find the general solution of the inhomogeneous equation y" + 3y' = te'.

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Q: Find the function that solves the initial value problem dy 10x + 3, y(1) = 0. dx y(x)

A: According to question,Given differential equation,dydx = -10x+3,y1 = 0

Q: Solve the initial value problem: dy/dx= (1/(2sqrt(x)))+2 y(1)=3

A: Solving the initial value problem.

Q: Find the solution of the initial value problem subject to the indicated initial condition in terms…

A: solution :-

Q: Solve the differential eqution y'-y=7e^x

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Q: Find the general solution of the differential equation. (Use C for the constant of integration).…

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Q: - ydx + (x ++xy )dy= 0

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Q: Solve the initial value problem given below. dy - 3y (-2 – y) dx

A: To Determine: solve the initial value problem.

Q: Solve the initial value problems for y as a functionof x. (x2 + 1)2 dy/dx = √x2 + 1, y(0) = 1

A: x2+12dydx=x2+1⇒dydx=x2+1x2+12⇒dydx=1x2+132⇒dy=1x2+132 dx Now integrating on both sides, we get…

Q: Find the value of k for which the constant function x(t) = k is a solution of the differential dx +…

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Q: Determine whether the equation (ye™y . 1 - =)dx + (xe®Y + y2 is exact. If so, solve the initial…

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Q: Use the method of steps to solve the delay differential equation dx x(t – 1) + 3; x(t) = 1 V…

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Q: x (xdx + ydy) + y (xdy – ydæ) = 0

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Q: solve the initial value problem dx/dt=x-x^{3} with x(0)=1 Please provide valid answer

A: Given differential equation is

Q: solve the bernoulli equation dx +1x' + = 0 +tx dt

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s). f…

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Q: Solve the initial value problem dy y = 5e" + 28e5* dx with y(0) = 8.

A: The solution of differential equation is given as follows :

Q: find the general solution of the differentialequation and check the result by differentiation.dy/ dt…

A: The given differential equation: dydt=x32 Integrate both sides of the differential equation with…

Q: Solve the initial-value problem for y as a function of x. (25−x^2)dy/dx=1, y(0)=9 y=?

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Q: Find the general solution of the differential equation. Use C for the constant of integration. dy dx…

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