What is the solution for 2xy-9x^2+(2y+x^2+1)(dy)/(dx)=0,y(0)=3 ?

The solution for 2xy-9x^2+(2y+x^2+1)(dy)/(dx)=0,y(0)=3 is y=(-1-x^2+sqrt(x^4+12x^3+2x^2+49))/2

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2xy-9x^2+(2y+x^2+1)(dy)/(dx)=0,y(0)=3

2 x y - 9 x^{2} + (2 y + x^{2} + 1) \frac{d y}{d x} = 0, y (0) = 3

y = \frac{- 1 - x ^{2} + x ^{4} + 12 x ^{3} + 2 x ^{2} + 49}{2}

Solution steps

2 x y - 9 x^{2} + (2 y + x^{2} + 1) \frac{d y}{d x} = 0

Solve exact ODE:

y = \frac{- 1 - x ^{2} + x ^{4} + 12 x ^{3} + 2 x ^{2} + 49}{2}

y = \frac{- 1 - x ^{2} + x ^{4} + 12 x ^{3} + 2 x ^{2} + 49}{2}

\int 6 t^{5} d t

x^{2} y^{^{'}} - 3 x y - 2 y^{2} = 0

\frac{d y}{d t} + \frac{2}{t} y = t - 1 + \frac{y}{t}

y = 9 x^{\frac{5}{2}} - 7 x^{\frac{3}{2}}, at x = 4

\frac{d y}{d x} - 2 (x + 1)^{3} = \frac{4}{( x + 1 )} y

What is the solution for 2xy-9x^2+(2y+x^2+1)(dy)/(dx)=0,y(0)=3 ?
The solution for 2xy-9x^2+(2y+x^2+1)(dy)/(dx)=0,y(0)=3 is y=(-1-x^2+sqrt(x^4+12x^3+2x^2+49))/2