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Question Number 51840 by 33 last updated on 31/Dec/18

$$solve$$$$\frac{dy}{dx}+\frac{2y}{3x}=\frac{x}{\sqrt{y}}$$

Answered by ajfour last updated on 31/Dec/18

$$3x\sqrt{y}dy+2y\sqrt{y}dx=3x^{2}dx$$$$d\left(xy\sqrt{y}\right)=\frac{3}{2}{x}^{2}dx$$$$2xy\sqrt{y}=x^3+c.$$

Answered by tanmay.chaudhury50@gmail.com last updated on 31/Dec/18

$$\frac{3xdy+2ydx}{3x\times dx}=\frac{x}{\sqrt{y}}$$$$3x\sqrt{y}dy+2y^{\frac{3}{2}}dx=3x^{2}dx$$$$xd\left(2y^{\frac{3}{2}}\right)+2y^{\frac{3}{2}}d\left(x\right)=d\left(x^3\right)$$$$d\left(x\times 2y^{\frac{3}{2}}\right)=d\left(x^3\right)$$$$x\times 2y^{\frac{3}{2}}=x^3+c$$

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