First slide

Methods of solving first order first degree differential equations

Question

$A curve passes through (2, 3) and satisfying the D.E \int_{0}^{x} ty (t) d t = x^{2} y (x), x > 0 is$

Moderate

A

$x^{2} {+y}^{2} =13$
B

$y^{2} = \frac{9}{2} x$
C

$\frac{x^{2}}{8} + \frac{y^{2}}{18} =1$
D

$xy=C$

Solution

$\begin{array}{l} \int_{0}^{x} ty (t) dt = x^{2} y (x) \\ Differentiating w.r.t. x, we get \\ xy (x) + x^{2} y^{1} (x) = 0 \\ \to x \frac{dy}{dx} + y = 0 \\ \Rightarrow \log x + \log y = \log C \\ \Rightarrow xy = C \end{array}$

Get Instant Solutions

When in doubt download our app. Now available Google Play Store- Doubts App

Recieve an sms with download link

Doubts App

OR

SCAN ME

Doubts App

Doubts App