# 6.4: Problems

Problem $$\PageIndex{1}$$

Solve the following differential equation

$(1-x)y'(x)-y=0 \nonumber$

using 1) the separation of variables method and 2) the power series method, and prove that the two solutions are mathematically equivalent.

Problem $$\PageIndex{2}$$

Solve the following differential equation

$y''(x)-y(x)=0 \nonumber$

using 1) the method we have learned for second order ODEs with constant coefficients and 2) the power series method, and prove that the two solutions are mathematically equivalent.

Problem $$\PageIndex{1}$$

Solve the Laguerre equation with $$n=2$$ and $$n=3$$. Write down $$L_2(x)$$ and $$L_3(x)$$