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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

\int_{- 1}^{2} 1 + x^{2} d x

\frac{d}{d x} (cos (x) + x sin (x))

x y^{^{'}} - y^{2} = x y^{2}

f (x) = 8 sin^{3} (x)

\frac{d}{d x} (\frac{( 5 x ^{5} - 3 )}{( - 3 x ^{3} + 1 )})

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