Home
Class 12
MATHS
If y = 5 cos x-3 s in x, prove that (d^2...

If `y = 5 cos x-3 s in x`, prove that `(d^2y)/(dx^2)+y=0`

Text Solution

AI Generated Solution

To prove that \(\frac{d^2y}{dx^2} + y = 0\) for the function \(y = 5 \cos x - 3 \sin x\), we will follow these steps: ### Step 1: Find the first derivative \(\frac{dy}{dx}\) Given: \[ y = 5 \cos x - 3 \sin x \] ...
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    NCERT ENGLISH|Exercise EXERCISE 5.5|18 Videos

  • APPLICATION OF INTEGRALS

    NCERT ENGLISH|Exercise EXERCISE 8.2|7 Videos

  • DETERMINANTS

    NCERT ENGLISH|Exercise All Questions|116 Videos

Similar Questions

Explore conceptually related problems

If y= A sin x+ B cos x , then prove that (d^2y)/(dx^2)+y=0 .

If x^my^n = (x + y)^(m+n) , prove that (d^2y)/(dx^2)=0 .

Given that y = 3 cos x + 2 sin x . Show that (d^(2)y)/(dx^(2)) + y = 0

If y=2 sin x+3cos x , show that (d^2y)/(dx^2)+y=0

If y=Acosn x+Bsinn x ,s howt h a t (d^2y)/(dx^2)+n^2y=0

If y= cot x, prove that (d^(2)y)/(dx^(2)) + 2y (dy)/(dx)= 0.

If y=acos(logx)+bsin(logx), prove that x^2(d^2y)/(dx^2)+\ x(dy)/(dx)+y=0

If x=costheta , y=s in^3theta , prove that y\ (d^2y)/(dx^2)+((dy)/(dx))^2=3\ s in^2theta(5\ cos^2theta-1) .

If y = e^(x) (sin x + cos x ) , prove that (d^(2) y)/( dx^(2)) - 2 (dy)/( dx) + 2 y = 0

If y=cos (sin x) , show that (d^2y)/(dx^2)+tan x""(dy)/(dx)+y cos^2 x=0