Solve differential equation and sketch the solution curves:

1. 1^st order ODE, non-linear, in standard differential form

2. Check for exact:

not exact

3. Try condition 3) on p.96

(function of y)

4. Integrating factor

5. Reduce ODE to exact by multiplication by

and solve as exact:

6. Find f :

7. General solution:

Check for suppressed solutions:

are suppressed solutions

> restart;

> with(plots):

> f:={seq(exp(x)*sin(y)^2+y*cos(y)- sin(y)=c/2,c=-10..10),y=Pi,y=2*Pi,y=-Pi,y=-2*Pi}:

> implicitplot(f,x=-3..4,y=-2*Pi..2*Pi,numpoints=5000);