What is the solution for (dy)/(dx)=(xsqrt(x^2+3))/(e^{2y)} ?

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

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(dy)/(dx)=(xsqrt(x^2+3))/(e^{2y)}

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

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

Solution steps

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

Solve separable ODE:

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

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

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