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

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

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

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

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

Solution steps

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

Solve separable ODE:

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

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

y^{^{'}} = \frac{x ^{3} y}{x ^{4} + 1}

8 x y^{3} d x + 12 x^{2} y^{2} d y = 0

\frac{d y}{d x} + 3 y = 0, y > 0

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

\frac{d y}{d x} = \frac{2 ln ( x )}{x y}

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