What is the solution for (dx)/(dy)=(2y+sec^2(y))/(2x) ?

The solution for (dx)/(dy)=(2y+sec^2(y))/(2x) is x=sqrt(y^2+tan(y)+c_{1)},x=-sqrt(y^2+tan(y)+c_{1)}

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(dx)/(dy)=(2y+sec^2(y))/(2x)

\frac{d x}{d y} = \frac{2 y + sec ^{2} ( y )}{2 x}

x = y^{2} + tan (y) + c_{1}, x = - y^{2} + tan (y) + c_{1}

Solution steps

\frac{d x}{d y} = \frac{2 y + sec ^{2} ( y )}{2 x}

Solve separable ODE:

x = y^{2} + tan (y) + c_{1}, x = - y^{2} + tan (y) + c_{1}

x = y^{2} + tan (y) + c_{1}, x = - y^{2} + tan (y) + c_{1}

What is the solution for (dx)/(dy)=(2y+sec^2(y))/(2x) ?
The solution for (dx)/(dy)=(2y+sec^2(y))/(2x) is x=sqrt(y^2+tan(y)+c_{1)},x=-sqrt(y^2+tan(y)+c_{1)}