Question

a)
find all possible solutions of y''+y'-6y=12t

b) solve initial value problem of y''+y'-6y=12t, y(0)=1,
y'(0)=0

Answer #1

Solve the initial value problem 8(t+1)dy/dt−6y=12t, for t>−1
with y(0)=11.

solve the initial value problem: y'''+y''-6y'=0 ; y(0)=1;
y'(0)=y''(0)=1

Solve the given initial-value problem.
y'' + 5y' −
6y =
12e2x, y(0)
= 1, y'(0) = 1

Solve the given initial-value problem.
y''' + 6y'' +
9y' = 0, y(0) = 0,
y'(0) = 1, y''(0) = −6

Solve the initial value problem y′′+6y′+9y=0, y(−1)=3,
y′(−1)=3.

solve the given initial value problem y''-5y'+6y=0, y(0)=3/5,
y'(0)=1

Solve the initial value problem 9(t+1) dy dt −6y=18t,
9(t+1)dydt−6y=18t, for t>−1 t>−1 with y(0)=14. y(0)=14. Find
the integrating factor, u(t)= u(t)= , and then find y(t)= y(t)=

Use the laplace transform to solve for the initial
value problem:
y''+6y'+25y=delta(t-7)
y(0)=0 y'(0)=0

Solve the initial-value problem. y"-6y'+9y=0; y(0)=2,
y'(0)=3
Given that y1=x2 is a solution to y"+(1/x)
y'-(4/x2) y=0, find a second, linearly independent
solution y2.
Find the Laplace transform. L{t2 *
tet}
Thanks for solving!

Use the method of Laplace transforms to solve the following
initial value problem. y'' + 6y' + 5y = 12e^t ; y(0) = −1, y'(0) =
7

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