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

Verified by Experts

`y=5" cos"x-3" sin"x`
`implies(dy)/(dx)=(d)/(dx)(5" cos"x-3" sin"x)= -5sinx-3cos x`
`implies(d^(2)y)/(dx^(2))=(d)/(dx)(-5" sin"x-3 cos x)`
`= -5 cos x+3 sin x `
`= -(5 cos x-3 sin x)= -y`
`implies(d^(2)y)/(dx^(2))+y=0 " " `Hence Proved.
Promotional Banner

Topper's Solved these Questions

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.8|6 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|23 Videos

  • Continuity and Differentiability

    NAGEEN PRAKASHAN ENGLISH|Exercise Exercies 5.6|11 Videos

  • APPLICATIONS OF INTEGRALS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 Videos

  • DETERMINANTS

    NAGEEN PRAKASHAN ENGLISH|Exercise Miscellaneous Exercise|19 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