What is the solution for (dy)/(dx)4y^2=(3x-15)/(3x+15) ?

The solution for (dy)/(dx)4y^2=(3x-15)/(3x+15) is y=\sqrt[3]{(-30ln(x+5)+3x+c_{1})/4}

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(dy)/(dx)4y^2=(3x-15)/(3x+15)

\frac{d y}{d x} 4 y^{2} = \frac{3 x - 15}{3 x + 15}

y = 3 \frac{- 30 ln ( x + 5 ) + 3 x + c _{1}}{4}

Solution steps

\frac{d y}{d x} 4 y^{2} = \frac{3 x - 15}{3 x + 15}

Solve separable ODE:

y = 3 \frac{- 30 ln ( x + 5 ) + 3 x + c _{1}}{4}

y = 3 \frac{- 30 ln ( x + 5 ) + 3 x + c _{1}}{4}

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

y^{^{'}} = 2.25 y

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

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

y^{^{'}} = x^{2} y^{- 3}

What is the solution for (dy)/(dx)4y^2=(3x-15)/(3x+15) ?
The solution for (dy)/(dx)4y^2=(3x-15)/(3x+15) is y=\sqrt[3]{(-30ln(x+5)+3x+c_{1})/4}