Find the solution of the given initial value problem in explicit form. 1 y' = (1 - 5x)y², y(0) = 8 y(x) =

Q: Solve the initial value problems.

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Q: t(t-1)dx t(t-1) = x(x + 1), x(2) = 2 dt

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Q: Find the exact solution to the initial value problem.

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Q: (iii) y" – y = (x+1)², y(0) = 1, y'(0) = 1. %3D %3D

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Q: Q=ht, he-h 2- = (10 و 1-(210

A: We have to solve the following initial value problem:                 y''-2y'+y=0,          y(0)=1,…

Q: 2. Solve the initial value problem 5 y"+y+y=g(t)=t-u/2(t) (t-n/2), y(0) = 0, y(0)=0.

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Q: VT - ỷ dx – VT-x dy = 0, y(0) V3

A: We have to solve given problem:

Q: y" + 4y = 4 sin(2x)+ 8 cos(2x), y(0) = 0, y' (0) = 1.

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Q: ´y′ − (t + 2ty) = 0, - e²² y(0) = 1

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Q: 1. Let A = F(t) %3D !3! 0. Find the solution of the initial value problem: X' = AX + F(t), X(0) n.…

A: Consider the given matrix. A=111111111,Ft=111,η=000 First, find the eigenvalue of matrix A.…

Q: Find the particular solution for each initial value problem.

A: Given the differential equation is By using separable variable method, 2y - 1 dy = x2 + 5  dx…

Q: dx dt dy dt x(0) = -1, y(0) = 1 -y + 3e-t 2х + Зу I|||

A: The solution is given as

Q: a) y" + 3y' +2.25y = -10e-1.5x, y(0) = 1, y'(0) = 0

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Q: find the solution of the given initial-value problem

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Q: a?u a?u = 4 at? -00 < x < 0 əx² u(x,0) = senx ,–-0 < x < 0 ди (x, 0) = 1, - 0 < x < 0 at

A: Use D'Alembert formula.

Q: dx = dt 6(x² + 1), + 1), x(/4) = 1

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Q: (v) y" – y = sech(x), y(0) = 0, y'(0) = 0. NOTE: sech(x) is the hyperbolic secant of x. In (v), it…

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Q: Find the particular solution for each initial value problem.

A: The given differential equation is dydx=5e-x-1 with initial condition y0=17. Solve the above…

Q: a.) 2y + y = 0, b.) y" - 10y' + 9y = 5t, y(0) = -3 y(0) = -1 and y' (0) = 2

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Q: dy (a) dx JE, y(1) = 2 dy (b) dt sin t + 1, y () =; dy (c) dx x +1 y(1) = 0

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Q: Consider the initial value problem y +y=1- (0) = 4 y(0) = yo-

A: We have to solve given initial value problem:

Q: (r³ + xy²)dx + (x²y + y*)dy = xdy + ydx.

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Q: y' = (3x² – e*)/(2y – 5), y(0) = 1

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Q: Find the solution of the given initial value problem.

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