If y =3 cos ( log x ) + 4 sin ( log x ), then show that $x^{2} \frac{d^{2} y}{{dx}^{2}} + x \frac{dy}{dx} + y = 0$

Solution

y = 3 cos ( log x ) + 4 sin ( log x )

Differentiating the above function with respect to x, we have,

$\frac{dy}{dx} = \frac{- 3 \cos (\log x)}{x} + \frac{4 \cos (\log x)}{x} x \frac{dy}{dx} = - 3 \cos (\log x) + 4 \cos (\log x)$

Again differentiating the above function with respect to x, we have,

$x \frac{d^{2} y}{{dx}^{2}} + \frac{dy}{dx} = \frac{- 3 \cos (\log x)}{x} - \frac{4 \sin (\log x)}{x} \Rightarrow x^{2} \frac{d^{2} y}{{dx}^{2}} + x \frac{dy}{dx} = - (3 \cos (\log x) + 4 \sin (\log x)) \Rightarrow x^{2} \frac{d^{2} y}{{dx}^{2}} + x \frac{dy}{dx} = - y \Rightarrow x^{2} \frac{d^{2} y}{{dx}^{2}} + x \frac{dy}{dx} + y = 0$

For Daily Free Study Material Join wiredfaculty

Continuity And Differentiability

If y =3 cos ( log x ) + 4 sin ( log x ), then show that $x^{2} \frac{d^{2} y}{{dx}^{2}} + x \frac{dy}{dx} + y = 0$

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

Phone Number

Email Address

Location

For Daily Free Study Material Join wiredfaculty

Continuity And Differentiability

If y =3 cos ( log x ) + 4 sin ( log x ), then show that x2 d2ydx2 + x dydx + y = 0

Some More Questions From Continuity and Differentiability Chapter

Mock Test Series

NCERT Sample Papers

Entrance Exams Preparation

If y =3 cos ( log x ) + 4 sin ( log x ), then show that $x^{2} \frac{d^{2} y}{{dx}^{2}} + x \frac{dy}{dx} + y = 0$