y^2*cos(x) = a^2*sin(x*y^2)
y^2*cos(x) - a^2*sin(x*y^2) = 0
Берем производную от функций, и от y, как от функции y(x).
2y*cos(x)*y' + y^2*(-sin(x)) - a^2*cos(x*y^2)*(y^2 + x*2y*y') = 0
Объединяем y' отдельно, остальное отдельно
2y*cos(x)*y' - a^2*cos(x*y^2)*x*2y*y' = a^2*cos(x*y^2)*y^2 + y^2*sin(x)
![y'=\frac{a^2*cos(x*y^2)*y^2 + y^2*sin(x)}{2y*cos(x) - a^2*cos(x*y^2)*x*2y} =\frac{a^2*y*cos(x*y^2) + y*sin(x)}{2cos(x) - 2a^2*x*cos(x*y^2)}](https://tex.z-dn.net/?f=y%27%3D%5Cfrac%7Ba%5E2%2Acos%28x%2Ay%5E2%29%2Ay%5E2+%2B+y%5E2%2Asin%28x%29%7D%7B2y%2Acos%28x%29+-+a%5E2%2Acos%28x%2Ay%5E2%29%2Ax%2A2y%7D+%3D%5Cfrac%7Ba%5E2%2Ay%2Acos%28x%2Ay%5E2%29+%2B+y%2Asin%28x%29%7D%7B2cos%28x%29+-+2a%5E2%2Ax%2Acos%28x%2Ay%5E2%29%7D)