First slide

Methods of solving first order first degree differential equations

Question

$The solution of ydx - xdy + 3 x^{2} y^{2} e^{x^{3}} dx = 0 is$

Moderate

A

$\frac{y}{x} + e^{x^{3}} = c$
B

$\frac{x}{y} {-e}^{x^{3}} = c$
C

$\frac{x}{y} {+e}^{x^{3}} = c$
D

$\frac{y}{x} {-e}^{x^{3}} = c^{3}$

Solution

$\int \frac{ydx-xdy}{y^{2}} + \int 3 e^{x^{3}} . x^{2} dx$
$\Rightarrow \int d (x / y) + \int e^{x^{3}} \cdot 3 x^{2} dx \Rightarrow \frac{x}{y} + e^{x^{3}} = c$

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