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}

y^{^{'}} = 8 x sec (y)

e^{x} tan (y) d x + (1 - e^{x}) sec^{2} (y) d y = 0

x cos (y) + 1 - x^{2} sin (y) y^{^{'}} = 0

(5 x + 4) + (5 y - 5) y^{^{'}} = 0

y^{^{'}} (x) = (1 - y^{2}) tan (x), y (0) = 3

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