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The general solution of the differential equation $\frac{y d x-x d y}{y}=0$ is
(a) $x y=c$
(b) $x=c y^2$
(c) $y=c x$
(d) $y=c x^2$
(a) $x y=c$
(b) $x=c y^2$
(c) $y=c x$
(d) $y=c x^2$
Solution:
1683 Upvotes
Verified Answer
The differential equation is $\frac{\mathrm{ydx}-\mathrm{xdy}}{\mathrm{y}}=0$ or $\frac{\mathrm{dx}}{\mathrm{x}}-\frac{\mathrm{dy}}{\mathrm{y}}=0$
Integrate, $\int \frac{d x}{x}-\int \frac{d y}{y}=($ say $) c^{\prime}$ $\log x-\log y=c^{\prime} \quad$ or $\frac{x}{y}=c^{\prime}$
Put $\mathrm{c}^{\prime}=\frac{1}{\mathrm{c}}, \frac{\mathrm{x}}{\mathrm{y}}=\frac{1}{\mathrm{c}} \mathrm{y}=\mathrm{cx}$ is the reqd solution.
Option (c) is correct.
Integrate, $\int \frac{d x}{x}-\int \frac{d y}{y}=($ say $) c^{\prime}$ $\log x-\log y=c^{\prime} \quad$ or $\frac{x}{y}=c^{\prime}$
Put $\mathrm{c}^{\prime}=\frac{1}{\mathrm{c}}, \frac{\mathrm{x}}{\mathrm{y}}=\frac{1}{\mathrm{c}} \mathrm{y}=\mathrm{cx}$ is the reqd solution.
Option (c) is correct.
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