2.2.1-2 1g

Solve the following differential equation and sketch the solution curves:

Solution:

1. Rewrite equation in normal form:

1^st order, non-linear, non-separable

check for exact:

2. Rewrite equation in standard differential form:

Not exact. Try for integrating factor:

function of y only

Then integrating is

Convert equation to exact by multiplying by integrating factor:

Find function :

General Solution:

Solution curves:

> restart;

> f:={seq(exp(i/x/2)/x,i=-6..6)}:

> plot(f,x=-2..2,y=-10..10,color=black);