dx + 3x dt cos(5t) %3D with x(0) = 1. x(t) = %3D

Q: Solve the initial value problems.

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Q: Solve the initial value problem. dt t-1 = 4, r(1) = 5 %3D Or-+7t + 15 6. -55 Or + 7t - 5 r= 3t + 7t…

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Q: f'(x) = z - 4r+ 12z + 12 and f(0) = 7.

A: f'x=x15-4x3+12x+12  &  f0=7 Integrating on both sides with respect to x, we get ∫f'x…

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

A: We have to find solution of given differential equation. We will first find Complementary solution…

Q: 9y" - 30y' + 25y 0, y'(0) = 1, y(0) = 3 |

A: Solution:- Given differential equation is            9y''-30y'+25y=0 , y'(0) = 1   , y(0) = 3Given…

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

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Q: 4". Sy' 8y Sx'e* y10)=8, y'l0).S X-

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Q: du 17. t = t² + 3u, t> 0, u(2) = 4 dt

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Q: Use the method of Laplace transforms to solve the given initial value problem. Here, x' and y'…

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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: 4y" +5y'+3y = 0, y(0) = -1, y' (0) = 1

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Q: Solve the inizial Nalve pooblem 2xe %3D yco)3=

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Q: y' = 3y2 y(2) = 0

A: For first order differential equation of variables x and y, if it is possible to arrange all the x…

Q: Solve the initial value problem. dy +y = 10 cos 0, 0 > 0, y(x) = 1 op

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Q: Solve the initial value problem y' + y = x y(1) = 3 Z+5 y(x) :

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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: (²-) = (0)x 'x (₁-5) = x 9

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Q: 8y" – 10y' + 3y= 0, y(0) = 2, y'(0) = 1

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Q: + 14y + 50y = 0, y(0) = 2, y(0) = -17

A: We have to solve given problem: