Solving Separable Equations: y'=xcos^(2)y

[btnh]

I am just supposed to find the general solution, in an explicit form if possible.

y'=xcos^(2)y

Thanks!

 

[sennyk]

Do your own HW.

I am just supposed to find the general solution, in an explicit form if possible.

y'=xcos^(2)y

Thanks!

This problem can be answered by someone with a strong grasp of calculus I. Get your calculus I book out.

Ken

 

[Matthew Rodman]

Multiply both sides by $$\sec^2{y}$$, to get

$$y^{\prime} \sec^2{y} = x$$

Now, integrate both sides w.r.t. x to get

$$\tan{y} = \frac{x^2}{2} + \kappa$$

where $$\kappa$$ is a constant.