d'y = 4 sec 2x tan 2x, y' (0) = 4, y (0) = -1 dx?

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: ´y′ − (t + 2ty) = 0, - e²² y(0) = 1

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

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

A: The solution is given as

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: 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: 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:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.