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

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

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(dy)/(dt)=(2t+sec^2(t))/(2y)

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

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

Solution steps

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

Solve separable ODE:

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

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

\int (cos (3 x) - sin (5 x)) d x

\frac{d}{d x} (8 csc (x) + 2)

f (t) = - 16 t^{2}

\int \frac{- x}{x + 1} d x

5 + x

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