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

1.	Find:2x dy/dx = x(x + 1)y3
Answer» 2x \(\frac{dy}{dx}=x(x+1)y^3\) ⇒ \(\frac{2dy}{dx}=\frac{x(x+1)}xdx\) (solved by variable separation) ⇒ \(\int\limits\frac2{y^3}dy=\int\limits(x+1)dx\) ⇒ 2 x \(\frac{y^{-3+1}}{-3+1}=\frac{x^2}2+x-c,\) where -c is an integral constant. ⇒ -1/y² = x²/2 + x - c ⇒ \(\frac{x^2}2+x+\frac1{y^2}=c\)

Answer»

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

⇒ \(\frac{2dy}{dx}=\frac{x(x+1)}xdx\) (solved by variable separation)

⇒ \(\int\limits\frac2{y^3}dy=\int\limits(x+1)dx\)

⇒ 2 x \(\frac{y^{-3+1}}{-3+1}=\frac{x^2}2+x-c,\) where -c is an integral constant.

⇒ -1/y² = x²/2 + x - c

⇒ \(\frac{x^2}2+x+\frac1{y^2}=c\)

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

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