What is the solution for (dy)/(dx)=((2x+sec^2(x)))/(2y),y(0)=-6 ?

The solution for (dy)/(dx)=((2x+sec^2(x)))/(2y),y(0)=-6 is y=-sqrt(x^2+tan(x)+36)

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(dy)/(dx)=((2x+sec^2(x)))/(2y),y(0)=-6

\frac{d y}{d x} = \frac{( 2 x + sec ^{2} ( x ) )}{2 y}, y (0) = - 6

y = - x^{2} + tan (x) + 36

Solution steps

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

Solve separable ODE:

y = - x^{2} + tan (x) + 36

y = - x^{2} + tan (x) + 36

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What is the solution for (dy)/(dx)=((2x+sec^2(x)))/(2y),y(0)=-6 ?
The solution for (dy)/(dx)=((2x+sec^2(x)))/(2y),y(0)=-6 is y=-sqrt(x^2+tan(x)+36)