Elementary Differential Equations Problems:
1) Find the solution of the initial value
problem of y" + 3y' = 0, y(0) = -2, y'(0) = 3
2) Find the general solution of the equation
4y" - 9y = 0
3) Find the general solution of the equation
dy/dt = 2t(y – 2y2)
4) Given the second order linear homogeneous
equation y"- 2y' + y = 0,
a) Verify that y1(t) = e^t and
y2(t) = t e^t are solutions of the...
Consider the following differential equation:
x2y"-2xy'+(x2+2)y=0
Given that y1=x cos x is a solution, find a second
linearly independent solution to the differential equation.
Write the general solution.
x2 y" + (x2+x) y’
+(2x-1) y = 0,
Find the general solution of y1 with
r1 and calculate the coefficient up to
c4 and also find the general expression of the
recursion formula, (recursion formula for
y1)
Find the general solution of y2 based on
theorem 4.3.1. (Hint, set d2 = 0)
Power series
Find the particular solution of the differential equation:
(x^2+1)y"+xy'-4y=0 given the boundary conditions x=0, y=1 and y'=1.
Use only the 7th degree term of the solution. Solve for y at x=2.
Write your answer in whole number.