Question

The differential equation whose general solution is $y=A\cos \left(x+3\right),$ where $A$ is arbitrary constant is

• A. $\cot \left(x+3\right)y_1+y=0$
• B. $\tan \left(x+3\right)y_1+y=0$
• C. $\cot \left(x+3\right)y_1-y=0$
• D. $\tan \left(x+3\right)y_1-y=0$

Answer 1

The correct option is A $\cot \left(x+3\right)y_1+y=0$

Given,

$y=A\cos \left(x+3\right)$......(1).

Differentiating both sides w.r.t $x$ we get,

$\Rightarrow \frac{dy}{dx}=-A\sin (x+3)$

$\Rightarrow \frac{dy}{dx}=-\frac{y\times \sin (x+3)}{\cos (x+3)}$ [ Using (1) ]

$\Rightarrow y_1\cot (x+3)+y=0$