What is the solution for 4(dy)/(dx)=(e^ysin^2(x))/(ysec(x)) ?

The solution for 4(dy)/(dx)=(e^ysin^2(x))/(ysec(x)) is y=-\W((sin^3(x)+c_{1})/(12e))-1

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4(dy)/(dx)=(e^ysin^2(x))/(ysec(x))

4 \frac{d y}{d x} = \frac{e ^{y} sin ^{2} ( x )}{y sec ( x )}

y = - W (\frac{sin ^{3} ( x ) + c _{1}}{12 e}) - 1

Solution steps

4 \frac{d y}{d x} = \frac{e ^{y} sin ^{2} ( x )}{y sec ( x )}

Solve separable ODE:

y = - W (\frac{sin ^{3} ( x ) + c _{1}}{12 e}) - 1

y = - W (\frac{sin ^{3} ( x ) + c _{1}}{12 e}) - 1

\frac{d y}{d x} + x \cdot y = x \cdot y^{2}

y^{^{'}} = 0.1044 \cdot y, y (0) = 100000

\frac{d y}{d x} = \frac{8 y}{9 x}

y^{^{'}} = (1 + cos (x)) y, y (0) = 1

What is the solution for 4(dy)/(dx)=(e^ysin^2(x))/(ysec(x)) ?
The solution for 4(dy)/(dx)=(e^ysin^2(x))/(ysec(x)) is y=-\W((sin^3(x)+c_{1})/(12e))-1