Home
Class 12
MATHS
If y=3\ e^(2x)+2\ e^(3x) , prove that (d...

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

Text Solution

AI Generated Solution

To prove that \(\frac{d^2y}{dx^2} - 5\frac{dy}{dx} + 6y = 0\) for the function \(y = 3e^{2x} + 2e^{3x}\), we will follow these steps: ### Step 1: Find the first derivative \( \frac{dy}{dx} \) Given: \[ y = 3e^{2x} + 2e^{3x} \] ...
Doubtnut Promotions Banner Mobile Dark
|

Topper's Solved these Questions

  • FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|393 Videos

  • INCREASING AND DECREASING FUNCTION

    RD SHARMA|Exercise Solved Examples And Exercises|232 Videos

Similar Questions

Explore conceptually related problems

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

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

Knowledge Check

  • If y= 3e^(2x)+ 2e^(3x) ,then (d^(2)y)/(dx^(2))-5(dy)/(dx) =

    A
    6y
    B
    `-6y `
    C
    ` 3y `
    D
    ` -3y `

  • If y= x^(2) e^(x) ,then ( d^(2)y)/(dx^(2)) -(dy)/(dx) =

    A
    ` (x+1) e^(x)`
    B
    ` -(x+1) e^(x) `
    C
    ` 2(x+1) e^(x)`
    D
    ` -2( x+1) e^(x) `

    • Similar Questions

    Explore conceptually related problems

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

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

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

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

    If y=a+(b)/(x) ; prove that x(d^(2)y)/(dx^(2))+2(dy)/(dx)=0

    If y=x^(2)e^(x),"show that "(d^(2)y)/(dx^(2))-(dy)/(dx)-2(x+1)e^(x)=0

    Home
    Profile