# (y')^2+y^2=-2 why this equation has no general solution ?

1. ### young_eng

8
hi

(y')^2+y^2=-2
why this differential equation has no general solution ?

2. ### Pengwuino

7,118
It's non-linear. Having a general solution for these types of equations is the exception, not the rule.

Not that there isn't a general solution because I don't know. It's just that non-linear equations rarely have general solutions

3. ### Dickfore

Because the lhs is necessarily non-negative (sum of squares), whereas the lhs is negative. You can have a solution in complex numbers.

4. ### jackmell

Why not just solve it the regular way:

$$\frac{dy}{\sqrt{-2-y^2}}=\pm dx$$