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

The solution for 2xy^3dx+3x^2y^2dy=0,y(1)=2 is y=(c_{1})/(x^{2/3)}

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

2 x y^{3} d x + 3 x^{2} y^{2} d y = 0, y (1) = 2

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

Solution steps

2 x y^{3} d x + 3 x^{2} y^{2} d y = 0

Solve separable ODE:

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

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

5 x \frac{d y}{d x} = 6 (7 - 3 y)

y^{^{'}} + 5 y = 50

\frac{d y}{d x} = 3 x^{6} y, y > 0

y^{^{'}} - 2 y = 2 y^{\frac{1}{2}}, y (0) = 1

\frac{d P}{d t} = 8 Pt, P (1) = 2

What is the solution for 2xy^3dx+3x^2y^2dy=0,y(1)=2 ?
The solution for 2xy^3dx+3x^2y^2dy=0,y(1)=2 is y=(c_{1})/(x^{2/3)}