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}

y^{^{'}} = 6 x y - 2 x

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

v^{2} x d x + v x^{2} d v + vx d x + x^{2} d v = vx d x - x d x

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

\frac{d y}{d x} = x^{3} (y - 2), y (0) = 4

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