Home
Class 12
MATHS
y=ae^(mx)+be^(-mx) satisfies which of th...

`y=ae^(mx)+be^(-mx)` satisfies which of the following differential equation?

A

`(dy)/(dx)+my=0`

B

`(dy)/(dx)-my=0`

C

`(d^(2)y)/(dx^(2))-m^(2)y=0`

D

`(d^(2)y)/(dx^(2))+m^(2)y=0`

Text Solution

AI Generated Solution

To determine which differential equation the function \( y = ae^{mx} + be^{-mx} \) satisfies, we will follow these steps: ### Step 1: Differentiate \( y \) with respect to \( x \) Given: \[ y = ae^{mx} + be^{-mx} \] ...
Promotional Banner

Similar Questions

Explore conceptually related problems

Number of straight lines which satisfy the differential equation (dy)/(dx)+x((dy)/(dx))^2-y=0 is

If y(x) satisfies the differential equation y'-y tan x=2x and y(0)=0 , then

Which of the following is a differential equation of the family of curves y=Ae^(2x)+Be^(-2x)

The general solution of a differential equation is y= ae ^(bx+ c) where are arbitrary constants. The order the differential equation is :

The differential equation y=px+f(p) , …………..(i) where p=(dy)/(dx) ,is known as Clairout's equation. To solve equation i) differentiate it with respect to x, which gives either (dp)/(dx)=0 rArr p =c ………….(ii) or x+f^(i)(p)=0 …………(iii) The singular solution of the differential equation y=mx + m-m^(3) , where m=(dy)/(dx) , passes through the point.

The equation of the curve through the point (1,0) which satisfies the differential equatoin (1+y^(2))dx-xydy=0 , is

If y(x) satisfies the differential equation y^(prime)-ytanx=2xs e c x and y(0)=0 , then

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

The value of the constant 'm' and 'c' for which y = mx + c is a solution of the differential equation (d^2y/dx^2) - 3 (dy/dx) -4y = -4x is:

If xy = ae^(x) + be^(-x) satisfies the equation Axy'' +By' = xy , then |A-B| is__________.