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

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The discussion focuses on solving the separable differential equation y' = x cos²(y). The explicit general solution is derived by multiplying both sides by sec²(y), leading to the integral tan(y) = (x²/2) + κ, where κ is a constant. This method requires a solid understanding of calculus, particularly integration techniques. The solution emphasizes the importance of manipulating the equation to facilitate integration.

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  • Ability to manipulate and rearrange equations for integration
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I am just supposed to find the general solution, in an explicit form if possible.

y'=xcos^(2)y

Thanks!
 
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Do your own HW.

btnh said:
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
 
Multiply both sides by [tex]\sec^2{y}[/tex], to get

[tex]y^{\prime} \sec^2{y} = x[/tex]

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

[tex]\tan{y} = \frac{x^2}{2} + \kappa[/tex]

where [tex]\kappa[/tex] is a constant.
 

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