What is the solution for (dy)/(dx)=(e^{8y+sqrt(x)})/(sqrt(x)),x>0 ?

The solution for (dy)/(dx)=(e^{8y+sqrt(x)})/(sqrt(x)),x>0 is y=-(ln(-16e^{sqrt(x)}-c_{1}))/8

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(dy)/(dx)=(e^{8y+sqrt(x)})/(sqrt(x)),x>0

\frac{d y}{d x} = \frac{e ^{8 y + x}}{x}, x > 0

y = - \frac{ln ( - 16 e ^{x} - c _{1} )}{8}

Solution steps

\frac{d y}{d x} = \frac{e ^{8 y + x}}{x}

Solve separable ODE:

y = - \frac{ln ( - 16 e ^{x} - c _{1} )}{8}

y = - \frac{ln ( - 16 e ^{x} - c _{1} )}{8}

What is the solution for (dy)/(dx)=(e^{8y+sqrt(x)})/(sqrt(x)),x>0 ?
The solution for (dy)/(dx)=(e^{8y+sqrt(x)})/(sqrt(x)),x>0 is y=-(ln(-16e^{sqrt(x)}-c_{1}))/8