What is the solution for sqrt(x)(dy)/(dx)=e^{3y+sqrt(x)},x>0 ?

The solution for sqrt(x)(dy)/(dx)=e^{3y+sqrt(x)},x>0 is y=-(ln(-6e^{sqrt(x)}-c_{1}))/3

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sqrt(x)(dy)/(dx)=e^{3y+sqrt(x)},x>0

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

y = - \frac{ln ( - 6 e ^{x} - c _{1} )}{3}

Solution steps

x \frac{d y}{d x} = e^{3 y + x}

Solve separable ODE:

y = - \frac{ln ( - 6 e ^{x} - c _{1} )}{3}

y = - \frac{ln ( - 6 e ^{x} - c _{1} )}{3}

y^{^{'}} = 2 y, y (0) = 0

(2 x^{2} y + y^{3}) d x + (x y^{2} + 2 x^{3}) d y = 0

\frac{d y}{d x} = a y (1 - y)

y^{^{'}} = - 8 x^{2} y

4 x y^{^{'}} - 2 x y = 7 x

What is the solution for sqrt(x)(dy)/(dx)=e^{3y+sqrt(x)},x>0 ?
The solution for sqrt(x)(dy)/(dx)=e^{3y+sqrt(x)},x>0 is y=-(ln(-6e^{sqrt(x)}-c_{1}))/3