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

The solution for (dy)/(dx)=(3x+xy^2)/(2y+x^2y),y(2)=1 is y=sqrt((-5+2x^2)/3)

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

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

y = \frac{- 5 + 2 x ^{2}}{3}

Solution steps

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

Solve separable ODE:

y = \frac{- 5 + 2 x ^{2}}{3}

y = \frac{- 5 + 2 x ^{2}}{3}

\frac{d y}{d x} = 800 y

1 - x^{2} d y - x y d x = 0, y (1) = 2

\frac{d y}{d x} + y = 2, y (0) = 0

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

\frac{d y}{d x} = y (4 x^{2} + 4)

What is the solution for (dy)/(dx)=(3x+xy^2)/(2y+x^2y),y(2)=1 ?
The solution for (dy)/(dx)=(3x+xy^2)/(2y+x^2y),y(2)=1 is y=sqrt((-5+2x^2)/3)