What is the solution for sqrt(x)(dy)/(dx)=e^{4y+sqrt(x)},x>0 ?

The solution for sqrt(x)(dy)/(dx)=e^{4y+sqrt(x)},x>0 is y=-(ln(-8e^{sqrt(x)}-c_{1}))/4

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sqrt(x)(dy)/(dx)=e^{4y+sqrt(x)},x>0

x \frac{d y}{d x} = e^{4 y + x}, x > 0

y = - \frac{ln ( - 8 e ^{x} - c _{1} )}{4}

Solution steps

x \frac{d y}{d x} = e^{4 y + x}

Solve separable ODE:

y = - \frac{ln ( - 8 e ^{x} - c _{1} )}{4}

y = - \frac{ln ( - 8 e ^{x} - c _{1} )}{4}

y^{^{'}} = 3 y, y (1) = 5

(x^{2} - 3) \frac{d y}{d x} = x (y^{2} + 16)

y \frac{d y}{d x} - 4 x = 0

d x - \frac{1}{1 + y ^{2}} d y = 0

(x^{2} - 9) y^{^{'}} + x y = 0, y (5) = 1

What is the solution for sqrt(x)(dy)/(dx)=e^{4y+sqrt(x)},x>0 ?
The solution for sqrt(x)(dy)/(dx)=e^{4y+sqrt(x)},x>0 is y=-(ln(-8e^{sqrt(x)}-c_{1}))/4