JEE Main 2022 · 27 Jun · Shift 1 · Mathematics Q8

MathematicsSingle correct+4 / -1Question 8 of 90

If $\cos^{-1}\left(\dfrac y2\right)=\log_e\left(\dfrac x5\right)^5$ , $|y|<2$ , then :

x^2y''+xy'-25y=0

x^2y''-xy'-25y=0

x^2y''-xy'+25y=0

x^2y''+xy'+25y=0

Answer and worked solution

Official answer: D

Solve for y. $y=2\cos\left(5\ln\frac x5\right)$ .

Differentiate. $xy'=-10\sin\left(5\ln\frac x5\right)$ ; differentiating again, $xy'+x^2y''=-50\cos\left(5\ln\frac x5\right)=-25y$ .

So $x^2y''+xy'+25y=0$ .

(D)

JEE Main 2022 · 27 Jun · Shift 1, Mathematics question 8