First slide

Types of solutions of differential equations

Question

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

Easy

A

$y=xcot(c-x)$
B

$9cos-1(y/x)=c-x$
C

$y=xtan(c-x)$
D

$\frac{y^{2}}{x^{2}} =xtan(c-x)$

Solution

$\begin{array}{l} \frac{xdy - ydx}{x^{2} + y^{2}} = - dx \Rightarrow \int d ({Tan}^{- 1} (y / x)) = - \int d x \\ \Rightarrow {Tan}^{- 1} (y / x) = - x + c \Rightarrow y = xtan (c - x) \end{array}$

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