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