Consider the initial value problem Suppose we know that α= B = 3t ÿ' " = [2 4 31] [2t + a 3t² +B] is the unique solution to this initial value problem. Find ģ(t) and the constants a and B. g(t) = ÿ+ģ(t), ÿ(¹) = [2]. y(t) =

Q: Solve y (f) + 4y(t) = sin(t) – sin(t – 27)H(t– 27); y(0) = y (0) = 0 %3D

A: To find: Solve the given differential equation.

Q: 15. Let 2 √x 4 3/2 y' = 2y + 2xy' 13/2 Solve for y' when x = 1 and y = 4

A: NOTE: Refresh your page if you can't see any equations. . here we have x=1 and y=4

Q: Let A = (²2²) 22 Find et and the general solution to X' = AX + (1)

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Q: valuate the following: a. L {e3t + cos6t - e3t cos6t} b. L-1 {6s/(s2 + 25) + 3/(s2 + 25)} c. L-1…

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Q: 6z dy (78)a

A:

Q: Solve the nonlinear ODE Ay''+Byy''-y=0, where y=y(x) and A,B are constant

A: The given nonlinear ODE is: Ay"+Byy'-y=0 where y=yx and A,B are constants.

Q: Solve the initial value problem yy' + x = √√x² + y² with y(3) = √27. a. To solve this, we should use…

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Q: The general solution of y' = 10 can be written in the form Y =C D

A: We are solving the given problem by using the method of separation of variable.

Q: 37 The point x= 0 is an ordinary point of the following differential equations except. A. y"-xy'+2y=…

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Q: y(4) - 4y" + 6y" - 4y+y=0; y(0) = 0, y'(0) = 1, y'(0) = 0, y" (0) = 1

A: The Laplace transform is used to find the solution of the linear ordinary differential equation with…

Q: Find the general solution of the equation xy' = ky that is valid for x > 0.

A: We have to find y(x) for this equation which is valid for x>0. We use integration to solve this…

Q: 3 6. Let A = -4 Find the general solution of x' Ах.

A:

Q: Can you elaborate how to incorporate c into the solution. Like c=0? And how does f'(0)=7 and…

A: Solution below

Q: x²y" – 5xy'+9y = 2x

A:

Q: Find the general solution of EonC(2)'y/n-1),

A: ∑i=0nnCi(2)iy(n-i)

Q: Show that the substitution u = y' leads to a Bernoulli equation. Solve this equation. xy'' = y' +…

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Q: Use undetermined coefficients to find the particular solution to y'' – y' – by = 3e* Y,(t) =|

A: The given differential equation is  y"-y'-6y=3e3t  We have to find the particular solution of the…

Q: A = X' = AX. 00% FOTO

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Q: Q4. (a) Show that the substitution r= e' reduces the equation ar'y" + bry' + cy = g(x) to an…

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Q: (a) a²y + y sin r = xy. (b) y = x³y - 2y³. (c) y = e²-2y (d) y'= x² + y² xy

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Q: (D-1)x -8y = e :+(D+1)y = te'

A: Let us consider the given system of the differential equation then to solve the system of the…

Q: Find the general antiderivative of each function. (can check by taking the derivative) F(X)= 12x3…

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Q: (1) y "'+ y "– 2y = 3+2cosx

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Q: [Q3] Using the method of undetermined coefficients. (a) Solve y" - 2 y' - 3 y = 2e* -10 sin x, y(0)…

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Q: - Sapotri to solve 2x?y" – my + (x + 1)y = 0. n=0 12) Use y =

A: Given: 2x2y''-xy'+x+1y=0. To Do: Solve the given differential equation using y=∑n=0∞anxn+r.