Question

Solve the given initial-value problem.

* y''* + 5

Answer #1

solve the given initial value problem y''-5y'+6y=0, y(0)=3/5,
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''+5y'+6y=0, y(0)=1,
y′(0)=−1,
using Laplace transforms. When writing your answer limit
yourself to showing:
(i) The equation for L(y);
(ii) The partial fraction decomposition;
(iii) The antitransforms that finish the problem.

Solve the given initial-value problem. 5y'' + y' = −6x, y(0) =
0, y'(0) = −25
The answer I got is 155-155e^(-1/5)x-3x^2-30x

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

Find the solution of the given initial value problems.
6y"-5y'+y=0, y(0)=4 , y'(0)=0

Use Laplace transforms to solve the given initial value
problem.
y"-2y'+5y=1+t y(0)=0 y’(0)=4

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

Let
y’’ + 5y’ + 6y = 0
a) Show that for any constants A and B, y(x) = Ae^(-3x) +
Be^(-2x) solves the differential equation.
b) For what values of A and B will
y(x) =Ae^(-3x) + Be^(-2x) solve the initial value problem y’’
+ 5y’ + 6y = 0, y(0) = 0, and y’(0) = 9?

ﬁnd the solution of the given initial value problem
1. y''+y'−2y=0, y(0) =1, y'(0) =1
2. 6y''−5y'+y=0, y(0) =4, y'(0) =0
3. y''+5y'+3y=0, y(0) =1, y'(0) =0
4. y''+8y'−9y=0, y(1) =1, y'(1) =0

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