First slide

Methods of solving first order first degree differential equations

Question

$The solution of the differential equation y (1 + 3 x^{2} y e^{x^{3}}) d x = x d y is$

Moderate

A

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

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

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

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

Solution

$\frac{y d x - x d y}{y^{2}} + 3 x^{2} e^{x^{3}} d x = 0 \Rightarrow d (\frac{x}{y}) + d (e^{x^{3}}) = 0; Integrating on both sides \Rightarrow \frac{x}{y} + e^{x^{3}} = c$

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