The solution of the differential equation dy/dx=tan⁡y/x+y/x is

Correct answer: (B) sin⁡y/x=cx. dy/dx=tan⁡y/x+y/x y/x=v y=vx dy/dx=v+xdv/dx ∴ the given equation becomes v+xdv/dx=tan⁡ v+v 1/(tan⁡v)dv=1/x dx ∫cot⁡v dv=∫1/xdx log ⁡sin⁡v=log⁡x+log⁡c =log ⁡xc sin⁡v=xc sin⁡y/x=xc

Q63 / 150 · MHT CET 2017 · Mathematics

The solution of the differential equation $\frac{d y}{d x} = \tan (\frac{y}{x}) + \frac{y}{x}$ is

A
$\cos (\frac{y}{x}) = c x$
Correct answer
B
$\sin (\frac{y}{x}) = c x$
C
$\cos (\frac{y}{x}) = c y$
D
$\sin (\frac{y}{x}) = c y$

Solution

\frac{d y}{d x} = \tan (\frac{y}{x}) + (\frac{y}{x})

\frac{y}{x} = v

y = v x

\frac{d y}{d x} = v + x \frac{d v}{d x}

∴

the given equation becomes

v + x \frac{d v}{d x} = \tan v + v

\frac{1}{\tan v} d v = \frac{1}{x} d x

\int \cot v d v = \int \frac{1}{x} d x

\log |\sin v| = \log x + \log c

= \log (x c)

\sin v = x c

\sin (\frac{y}{x}) = x c

Hence, the correct answer is option: 'B'.

The solution of the differential equation dydx=tan⁡yx+yx is

Solution

Relevant Questions

The solution of the differential equation $\frac{d y}{d x} = \tan (\frac{y}{x}) + \frac{y}{x}$ is