What is the solution for (dy)/(dx)=((xsqrt(x^2+1)))/(ye^y) ?

The solution for (dy)/(dx)=((xsqrt(x^2+1)))/(ye^y) is y=\W(((x^2+1)^{3/2}+c_{1})/(3e))+1

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(dy)/(dx)=((xsqrt(x^2+1)))/(ye^y)

\frac{d y}{d x} = \frac{( x x ^{2} + 1 )}{y e ^{y}}

y = W \frac{( x ^{2} + 1 ) ^{\frac{3}{2}} + c _{1}}{3 e} + 1

Solution steps

\frac{d y}{d x} = \frac{( x x ^{2} + 1 )}{y e ^{y}}

Solve separable ODE:

y = W \frac{( x ^{2} + 1 ) ^{\frac{3}{2}} + c _{1}}{3 e} + 1

y = W \frac{( x ^{2} + 1 ) ^{\frac{3}{2}} + c _{1}}{3 e} + 1

y^{^{'}} = \frac{x e ^{x + y}}{y}

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

(t^{2} - 6 t + 5) y^{^{'}} = y

\frac{f ^{^{'}} ( x )}{f ( x )} = x e^{x}, f (0) = 4

y^{^{'}} = \frac{3 y ^{2} + 9}{( 2 x y )}

What is the solution for (dy)/(dx)=((xsqrt(x^2+1)))/(ye^y) ?
The solution for (dy)/(dx)=((xsqrt(x^2+1)))/(ye^y) is y=\W(((x^2+1)^{3/2}+c_{1})/(3e))+1