Find the general solution of a differential equation

[jimkochanski]

Homework Statement

I was asked to find the general solutions of the two following differential equations:

Q1. y'''[x] + 2 y''[x] + 5 y'[x] = 0

Q2. y''[x] + 6 y'[x] + 9 y[x] = 0

Homework Equations

See above.

The Attempt at a Solution

My answers to both problems were of the form y = f[x].

My professor informed me that the general solution for the differential equation y'''[x] + 2 y''[x] + 5 y'[x] = 0 should not have been of the form y = f[x], but should have been of the form y'[x] = f[x].

Is this conventional?

Would that mean the general solution of αy⁽⁵⁾[x] + βy'''[x] = 0 would be of the form y'''[x] = f[x]?

Thanks for sharing your insight/feedback!

Jim

 

[ehild]

The first equation does not include y(x), so it can be solved for y' as a second order de (use y'=z(x) and solve for z). After solving for z(x)=y'(x), you need to integral y' to get y. So the general solution is a function y=f(x) which contains three integration constants.

ehild