What is the solution for sqrt(x)(dy)/(dx)=e^{6y+sqrt(x)},x>0 ?

The solution for sqrt(x)(dy)/(dx)=e^{6y+sqrt(x)},x>0 is y=-(ln(-12e^{sqrt(x)}-c_{1}))/6

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sqrt(x)(dy)/(dx)=e^{6y+sqrt(x)},x>0

x \frac{d y}{d x} = e^{6 y + x}, x > 0

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 N}{d t} = k N (t)

\frac{d v}{d t} + 2 v = 32

\frac{d x}{d t} = 5 x - 3, x (2) = 1

\frac{d y}{d t} = a y + b

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

What is the solution for sqrt(x)(dy)/(dx)=e^{6y+sqrt(x)},x>0 ?
The solution for sqrt(x)(dy)/(dx)=e^{6y+sqrt(x)},x>0 is y=-(ln(-12e^{sqrt(x)}-c_{1}))/6