Solve the initial value problem: y'' + 4y' + 4y = 0; y(0) = 1,
y'(0) = 0.
Solve without the Laplace Transform, first, and then with the
Laplace Transform.
Solve the initial value problem dy/dx = −(2x cos(x^2))y +
6(x^2)e^(− sin(x^2)) , y(0) = −5
Solve the initial value problem dy/dt = (6t^5/(1 + t^6))y + 7(1
+ t^6)^2 , y(1) = 8.
Find the general solution of dy/dt = (2/t)*y + 3t^2* cos3t
(3 pts) Solve the initial value problem
25y′′−20y′+4y=0, y(5)=0, y′(5)=−e2.
(3 pts) Solve the initial value problem
y′′ − 2√2y′ + 2y = 0, y(√2) = e2, y′(√2) = 2√2e2.
Consider the second order linear equation t2y′′+2ty′−2y=0,
t>0.
(a) (1 pt) Show that y1(t) = t−2 is a solution.
(b) (3 pt) Use the variation of parameters method to obtain a
second solution and a general solution.
Consider the following initial value problem.
y''−4y = 0,
y(0) = 0, y'(0) = 5
(a) Solve the IVP using the characteristic equation method from
chapter 4.
(b) Solve the IVP using the Laplace transform method from chapter
7.
(Hint: If you don’t have the same final answer for each part, you’ve
done something wrong.)