What is the solution for sqrt(x)(dy)/(dx)=e^{6y+sqrt(x)} ?

The solution for sqrt(x)(dy)/(dx)=e^{6y+sqrt(x)} is y=-(ln(-12e^{sqrt(x)}-c_{1}))/6

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sqrt(x)(dy)/(dx)=e^{6y+sqrt(x)}

x \frac{d y}{d x} = e^{6 y + x}

y = - \frac{ln ( - 12 e ^{x} - c _{1} )}{6}

Solution steps

x \frac{d y}{d x} = e^{6 y + x}

Solve separable ODE:

y = - \frac{ln ( - 12 e ^{x} - c _{1} )}{6}

y = - \frac{ln ( - 12 e ^{x} - c _{1} )}{6}

\frac{d t}{d x} = \frac{ln ( x )}{x ^{2} t}

e^{y} y^{^{'}} = \frac{( ln ( t ) ) ^{2}}{t}

1 - x \frac{d y}{d x} = y^{2}

\frac{d y}{d x} x^{2} - y^{2} = 16

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

What is the solution for sqrt(x)(dy)/(dx)=e^{6y+sqrt(x)} ?
The solution for sqrt(x)(dy)/(dx)=e^{6y+sqrt(x)} is y=-(ln(-12e^{sqrt(x)}-c_{1}))/6