- #1

davon806

- 148

- 1

## Homework Statement

Hi,I am learning to solve 2nd-order differential eq.

Suppose I have a equation

dy/dx - 3x = 0...(1)

Then dy/dx = 3x -----> x = 3(x^2)/2

Now if I have a 2nd order ODE such that:

d^2y/dx^2 = 3....(2)

Then it could be solved by integrating both sides wrt x twice,which yields

y = 3(x^2)/2 + Ax + B

Now,consider the case:

d^2y/dx^2 -6dy/dx + 9 = 0...(3)

I know it could be solved by using the idea of auxiliary equation(Putting y = Ae^(sx) into the initial eq)

But,why it's not possible to solve (3) by using direct integration on both sides as in (1) and (2)?

I can illustrate it here:

d^2y/dx^2 = 6dy/dx - 9,then I integrate both sides wrt x

dy/dx = 6 -9x + A

y = 6x -9(x^2)/2 + Ax + B

It's obviously incorrect,the (6+A)x term vanishes in the 2nd order derivative.Can someone tell me what's wrong?(I mean on the idea)

Thx

## Homework Equations

## The Attempt at a Solution

I have illustrated it in the problem statement.