What is the solution for (dy)/(dx)=(3x+1)/(4y) ?

The solution for (dy)/(dx)=(3x+1)/(4y) is y=(sqrt(3x^2+2x+c_{1)})/2 ,y=-(sqrt(3x^2+2x+c_{1)})/2

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(dy)/(dx)=(3x+1)/(4y)

\frac{d y}{d x} = \frac{3 x + 1}{4 y}

y = \frac{3 x ^{2} + 2 x + c _{1}}{2}, y = - \frac{3 x ^{2} + 2 x + c _{1}}{2}

Solution steps

\frac{d y}{d x} = \frac{3 x + 1}{4 y}

Solve separable ODE:

y = \frac{3 x ^{2} + 2 x + c _{1}}{2}, y = - \frac{3 x ^{2} + 2 x + c _{1}}{2}

y = \frac{3 x ^{2} + 2 x + c _{1}}{2}, y = - \frac{3 x ^{2} + 2 x + c _{1}}{2}

\int_{0}^{1} \frac{5 x ^{4}}{1 + x ^{5}} d x

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What is the solution for (dy)/(dx)=(3x+1)/(4y) ?
The solution for (dy)/(dx)=(3x+1)/(4y) is y=(sqrt(3x^2+2x+c_{1)})/2 ,y=-(sqrt(3x^2+2x+c_{1)})/2