Find:(y + 2)x dy/dx = x(x + 1) y3

1.	Find:(y + 2)x dy/dx = x(x + 1) y3
Answer» (y + 2)x\(\frac{dy}{dx}\) = x(x + 1)y³----(i) ⇒ \(\frac{y+2}{y^3}dy=\frac{x(x+1)}xdx\) ⇒ \(\int(1/y^2+2/y^3)dy=\int(x+1)dx\) ⇒ -1/y - 1/y² + c = x²/2 + x ⇒ x²/2 + x + 1/y + 1/y² = c which is complete solution of given differential equation.

Answer»

(y + 2)x\(\frac{dy}{dx}\) = x(x + 1)y³----(i)

⇒ \(\frac{y+2}{y^3}dy=\frac{x(x+1)}xdx\)

⇒ \(\int(1/y^2+2/y^3)dy=\int(x+1)dx\)

⇒ -1/y - 1/y² + c = x²/2 + x

⇒ x²/2 + x + 1/y + 1/y² = c

which is complete solution of given differential equation.

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Find:(y + 2)x dy/dx = x(x + 1) y3

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