Solution of the differential equation : d y d x = 3 x 2 y 4 + 2 x y x 2 − 2 x 3 y 3 is Options: A . &nbsp x 2 y 2 + x 2 y = c B . &nbsp x 3 y 2 + x 2 y = c C . &nbsp x 3 y 2 + y 2 x = c D . &nbsp x 2 y 3 + x 2 y = c

Answer: Option B : B x 2 d y − 2 x 3 y 3 d y = 3 x 2 y 4 d x + 2 x y d x ⇒ x 2 d y − 2 x y d x = 3 x 2 y 4 d x + 2 x 3 y 3 d y ⇒ 2 x y d x − x 2 d y y 2 + 3 x 2 y 2 d x + 2 x 3 y d y = 0 ⇒ d ( x 2 y ) + d ( x 3 y 2 ) = 0 ⇒ x 2 y + x 3 y 2 = C

Solution of the differential equation : dydx=3x2y4+2xyx2−2x3y3 is

Discussion Forum : Differential Equations

Question -

Solution of the differential equation : $\frac{d y}{d x} = \frac{3 x^{2} y^{4} + 2 x y}{x^{2} - 2 x^{3} y^{3}}$ is

Options:

A .

x^{2} y^{2} + \frac{x^{2}}{y} = c

B .

x^{3} y^{2} + \frac{x^{2}}{y} = c

C .

x^{3} y^{2} + \frac{y^{2}}{x} = c

D .

x^{2} y^{3} + \frac{x^{2}}{y} = c

Answer: Option B
:
B

x^{2} d y - 2 x^{3} y^{3} d y = 3 x^{2} y^{4} d x + 2 x y d x \Rightarrow x^{2} d y - 2 x y d x = 3 x^{2} y^{4} d x + 2 x^{3} y^{3} d y \Rightarrow \frac{2 x y d x - x^{2} d y}{y^{2}} + 3 x^{2} y^{2} d x + 2 x^{3} y d y = 0 \Rightarrow d (\frac{x^{2}}{y}) + d (x^{3} y^{2}) = 0 \Rightarrow \frac{x^{2}}{y} + x^{3} y^{2} = C

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Discussion Forum : Differential Equations

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