2.2.5 #1a Solve the differential equation and sketch the solution curves:

Solution: 1. 1^st order, linear, non-homogeneous, with variable coefficients. Use variation of parameter formula. Rewrite equation in standard normal form for linear equation:

2. Integrating factor:

3. General solution:

4. Answer:

> restart;

> P:={seq((c/2)*exp(x)/x+exp(-x),c=-12..12)}:

> plot(P,x=-2..4,y=-4..5,color=black,axes=boxed);

Rewrite equation as

Then it follows that is also a solution (suppressed solution).