What is the solution for (dy)/(dx)=((2x+1))/(3y) ?

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

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(dy)/(dx)=((2x+1))/(3y)

\frac{d y}{d x} = \frac{( 2 x + 1 )}{3 y}

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

Solution steps

\frac{d y}{d x} = \frac{( 2 x + 1 )}{3 y}

Solve separable ODE:

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

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

\frac{d y}{d x} = 2 y - 4 x

f (x) = x^{2} (6 x + 1)^{3}

\int \frac{3}{x ^{- 1} + 1} d x

6 + 5 x

∣ x ∣, x^{2} - 2

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