First slide

Methods of solving first order first degree differential equations

Question

$General solution of x \frac{d y}{d x} + y = y^{2} x^{3} \cos x, is$

NA

A

$\frac{1}{x y} + x \sin x - \cos x = c$
B

$\frac{1}{x y} - x \sin x + \cos x = c$
C

$\frac{1}{x y} + x \cos x - \sin x = c$
D

$\frac{1}{x y} + x \sin x + \cos x = c$

Solution

$\begin{array}{l} Given x \cdot \frac{d y}{d x} + y = y^{2} x^{3} \cdot \cos x \Rightarrow \frac{(x d y + y d x)}{x^{2} y^{2}} = x \cdot \cos x d x \\ \Rightarrow d (- \frac{1}{x y}) = x \cdot \cos x d x \Rightarrow - \frac{1}{x y} = x \sin x + \cos x + c \end{array}$

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