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  • Solution of differential equation xdy – ydx = 0 represents: A. a rectangular hyperbola B. parabola whose vertex is at origin C. straight line passing through origin D. a circle whose centre is at origin

Solution of differential equation xdy – ydx = 0 represents:
A. a rectangular hyperbola
B. parabola whose vertex is at origin
C. straight line passing through origin
D. a circle whose centre is at origin

Answers (1)

\begin{aligned} &\text { Lets solve the differential equation }\\ &\begin{array}{l} x d y-y d x=0 \\ x d y=y d x \\ \Rightarrow \frac{d y}{y}=\frac{d x}{x} \\ \log y=\log x+c \\ \log x-\log y=c \\ \text { Using } \log a-\log b=\log a / b \\ \quad \Rightarrow \log \frac{y}{x}=c \\ \Rightarrow \frac{y}{x}=e^{c} \\ y=xe^{c} \end{array} \end{aligned}

\mathrm{e}^{\mathrm{c}}$  is constant because e is a constant and c is the integration constant let it be denoted as k hence

\\\mathrm{e}^{\mathrm{c}}=\mathrm{k}$ \\$y=k x$
\mathrm{y}=\mathrm{kx}$ is the equation of straight line and (0,0) satisfies the equation.

Option C is correct.

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infoexpert22

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