d²y 10. + 4y = 3 cos 2t dt2 y(0) = y'(0) = 0

Q: Solve the initial value problems.

A:

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

A:

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

A:

Q: Solve the general initial-value problem

A: Let U1(t)=1+3t and U2(t)=1+t3. The given differential equation is  t1+tu''-1+3tu'+3u=0    (Equation…

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.

A:

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

A:

Q: dy y? – 1 y(7) = 7 1 dx - y =

A:

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

A:

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

A:

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: Consider a nonnegative measurable funct that m({x € E : g(x) > M}) ≤ √ √ ² 9. M E Hint: Consider the…

A: Given a nonnegative measurable function g defined on E. If G is integrable over E. We have to prove…

Q: dx = dt 6(x² + 1), + 1), x(/4) = 1

A:

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

A:

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

A:

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

A:

Q: y² – x² 2 dy y(1) = –V2 %3D dx xy ху

A:

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

A:

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

A: