Solving Diff. Eqns: p(x)y''(x)+q(x)y'(x)+r(x)y(x)+a/b

[Logarythmic]

How can I solve the two differential equations

$$p(x)y''(x) + q(x)y'(x) + a \sin{y(x)} = 0$$

and

$$ay''(x) + p(x)y(x) + b \cos{y(x)} = 0$$

?

Are there any general method for solving an equation of the form

$$p(x)y''(x) + q(x)y'(x) + r(x)y(x) + a \sin{y(x)} = 0$$

or the similar one with cos instead of sin?

 

[arildno]

Yes, many. All of them belongs in the topic of numerical analysis.

 

[Logarythmic]

Yeah, but I've got a problem where I'm supposed to solve the first two analytically...