Home
Class 12
MATHS
If y = Ae^(mx) + Be^(nx), Show that (d^2...

If `y = Ae^(mx) + Be^(nx)`, Show that `(d^2 /dx^2 y)-(m+n)dy/dx+mny = 0`

Text Solution

Verified by Experts

The correct Answer is:
`-A mn e^(mx) - BN^2 e^(nx) + Amn e^(n x) + Bmn e^(nx) = 0`
Promotional Banner

Topper's Solved these Questions

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Short Answer Type Questions)(Section XI)|6 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Long Answer Type Questions)(Section XII)|4 Videos

  • CONTINUITY AND DIFFERENTIABILITY

    BETTER CHOICE PUBLICATION|Exercise SOLVED EXAMPLES (Short Answer Type Questions)(Section IX)|6 Videos

  • APPLICATIONS OF DERIVATIVES

    BETTER CHOICE PUBLICATION|Exercise PREVIOUS YEAR BOARD.S QUESTIONS FOR PRACTICE |73 Videos

  • DETERMINANTS

    BETTER CHOICE PUBLICATION|Exercise ASSIGNMENT (PREVIOUS YEAR.S BOARD QUESTIONS FOR PRACTICE )|45 Videos

Similar Questions

Explore conceptually related problems

Find the second order derivative of the following functions If y = ae^(mx) + be^(-mx) , prove that (d^2y)/(dx^2) - m^2y = 0

If y = ae^(mx) + be^-(mx) , then (d^2y)/(dx^2) =

IF y= x^x , show that [(d^2y/dx^2) -1/y(dy/dx)^2 - y/x = 0]

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

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

If y = e^(-ax) cos (bx + c) , show that (d^2y)/(dx^2) + 2a(dy)/(dx) + (a^2 + b^2) y = 0

If y = sin^-1x , then show that (1-x^2)(d^2y)/(dx^2)- x dy/dx = 0

If y = e^(acos^-1x), -1lexle1 , show that (1-x^2)(d^2y)/dx^2 - x(dy/dx) - a^2y = 0