ENGR 213 Lecture 10: practice_2

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2 Feb 2016
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Practice problems #2, ENGR 213
1.
Find a particular solution of the differential equation
y00 + 2y0+y=x2ex
using the method of undetermined coefficients.
2.
Find a particular solution of the differential equation
y00 +y= sin x
using variation of parameters.
3.
Find the general solution of the Cauchy-Euler equation
x2y00
xy0
3y= 0
4.
Solve the boundary value problem
(y00 +λy = 0
y0(0) = y0(L)=0
5.
The differential equation
y00 +2
xy0
y= 0
has one solution y1=ex/x. Use reduction of order to find a second linearly independent solution.
6.
Find the radius of convergence of the power series
X
n=0
xn+1
(2n+ 2)3n