Home
Class 12
MATHS
If y=500 e^(7x)+600 e^(-7x), show that (...

If `y=500 e^(7x)+600 e^(-7x)`, show that `(d^2y)/(dx^2)=49 y`

Text Solution

AI Generated Solution

To show that \(\frac{d^2y}{dx^2} = 49y\) for the function \(y = 500 e^{7x} + 600 e^{-7x}\), we will follow these steps: ### Step 1: Find the first derivative \( \frac{dy}{dx} \) Given: \[ y = 500 e^{7x} + 600 e^{-7x} \] ...
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=500e^(7x)+600e^(-7x) , shows that (d^(2)y)/(dx^(2))=49y .

If y=a e^(2x)+b e^(-x) , show that, (d^2y)/(dx^2)-(dy)/(dx)-2y=0 .

If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n y=0

If y=A e^(m x)+B e^(n x) , show that (d^2y)/(dx^2)-(m+n)(dy)/(dx)+m n y=0 .

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2 .

If e^y(x+1)=1 , show that (d^2y)/(dx^2)=((dy)/(dx))^2 .

If y=3\ e^(2x)+2\ e^(3x) , prove that (d^2y)/(dx^2)-5(dy)/(dx)+6y=0 .

If y=e^-x cos x , show that (d^2y)/(dx^2)= 2e^-x sin x

If y=e^(-x)cosx, show that (d^(2)y)/(dx^(2))=2e^(-x)sinx.