Home
Class 12
MATHS
If y=3e^(2x)+2e^(3x). Prove that (d^2y)/...

If `y=3e^(2x)+2e^(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: \[ y = 3e^{2x} + 2e^{3x} \] ...
Promotional Banner

Similar Questions

Explore conceptually related problems

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

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

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=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) ,then ( d^(2)y)/(dx^(2)) -(dy)/(dx) =

If y=e^(ax) sin be then prove that (d^2y)/(dx^(2))-2a(dy)/(dx)+(a^(2)+b^(2))y=0 .