What is the solution for (dy)/(dx)=e^{5y}cos(x/2) ?

The solution for (dy)/(dx)=e^{5y}cos(x/2) is y=-(ln(-10sin(x/2)-c_{1}))/5

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(dy)/(dx)=e^{5y}cos(x/2)

\frac{d y}{d x} = e^{5 y} cos (\frac{x}{2})

y = - \frac{ln ( - 10 sin ( \frac{x}{2} ) - c _{1} )}{5}

Solution steps

\frac{d y}{d x} = e^{5 y} cos (\frac{x}{2})

Solve separable ODE:

y = - \frac{ln ( - 10 sin ( \frac{x}{2} ) - c _{1} )}{5}

y = - \frac{ln ( - 10 sin ( \frac{x}{2} ) - c _{1} )}{5}

(x^{2} - 3) \frac{d y}{d x} - x (y - 1) = 0

x + 3 y^{2} x^{2} + 1 \frac{d y}{d x} = 0

x^{2} y \frac{d y}{d x} + 2 x y^{2} = 0

\frac{d y}{d x} = \frac{x sin ( x )}{y}, y (0) = - 1

\frac{d y}{d x} = a y

What is the solution for (dy)/(dx)=e^{5y}cos(x/2) ?
The solution for (dy)/(dx)=e^{5y}cos(x/2) is y=-(ln(-10sin(x/2)-c_{1}))/5