If y=a cos (log x)+b sin (log x),then x^2 y_2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(D) Given $y = a \cos(\log x) + b \sin(\log x)$.Differentiating with respect to $x$:$y_1 = \frac{dy}{dx} = -a \sin(\log x) \cdot \frac{1}{x} + b \cos(

Vedclass · Accepted Answer

$-y$

Vedclass · Answer

(D) Given $y = a \cos(\log x) + b \sin(\log x)$.Differentiating with respect to $x$:$y_1 = \frac{dy}{dx} = -a \sin(\log x) \cdot \frac{1}{x} + b \cos(\log x) \cdot \frac{1}{x}$$x y_1 = -a \sin(\log x) + b \cos(\log x)$.Differentiating again with respect to $x$:$x y_2 + y_1 = -a \cos(\log x) \cdot \frac{1}{x} - b \sin(\log x) \cdot \frac{1}{x}$Multiply by $x$:$x^2 y_2 + x y_1 = -[a \cos(\log x) + b \sin(\log x)]$Since $y = a \cos(\log x) + b \sin(\log x)$,we have:$x^2 y_2 + x y_1 = -y$.

If $y=a \cos (\log x)+b \sin (\log x)$,then $x^2 y_2+x y_1=$

Similar Questions

If $y=e^{m \sin ^{-1} x}$, then $(1-x^{2}) \frac{d^{2} y}{d x^{2}}-x \frac{d y}{d x}-k y=0$, where $k$ is equal to

If $y = \log(\log x)$,then $\frac{d^2y}{dx^2}$ is equal to

If $e^{y}(x+1)=1,$ show that $\frac{d^{2} y}{d x^{2}}=\left(\frac{d y}{d x}\right)^{2}$.

If $y = 3x^5 + 4x^4 + 2x + 3$,then

If the function $y = \sin^{-1} x$,then $\left(1-x^2\right) \frac{d^2 y}{d x^2}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module