You are Here: Home >< Maths

# 2nd order ODE system watch

1. Does anyone know how to solve this system of equations:
y''=z
z''=y
with boundary conditions y(0)=0, y(π/2)=1, z(0)=0, z(π/2)=1,

where y'' means d²y/dx² ?
2. (Original post by m277)
Does anyone know how to solve this system of equations:
y''=z
z''=y
with boundary conditions y(0)=0, y(π/2)=1, z(0)=0, z(π/2)=1,

where y'' means d²y/dx² ?
One way is to get y'''' = y which has general solution

y = Asinx + Bcosx + Cexp(x) + Dexp(-x)

and then

z = -Asinx - Bcosx + Cexp(x) + Dexp(-x)

Your boundary conditions then give you four equations in A,B,C,D
3. (Original post by RichE)
One way is to get y'''' = y which has general solution

y = Asinx + Bcosx + Cexp(x) + Dexp(-x)

and then

z = -Asinx - Bcosx + Cexp(x) + Dexp(-x)

Your boundary conditions then give you four equations in A,B,C,D
Thanks for this. I considered y''''=y but I didn't know what the general solution was.

How did you come up with this general solution? ie where did it come from?
4. (Original post by m277)
Thanks for this. I considered y''''=y but I didn't know what the general solution was.

How did you come up with this general solution? ie where did it come from?
From the auxiliary equation m^4 = 1
5. (Original post by RichE)
From the auxiliary equation m^4 = 1
ahhh, I see.

You factorise so that (m²-1)(m²+1)=0
and then use the auxilliary equation that I already know. So you end up having a linear combination of the complementary functions to m²-1=0 and m²+1=0.

Thank you. My tutor won't rip me to shreds now!

TSR Support Team

We have a brilliant team of more than 60 Support Team members looking after discussions on The Student Room, helping to make it a fun, safe and useful place to hang out.

This forum is supported by:
Updated: January 27, 2006
Today on TSR

### University open days

• Southampton Solent University
Sun, 18 Nov '18
Wed, 21 Nov '18
• Buckinghamshire New University
Wed, 21 Nov '18
Poll
Useful resources

### Maths Forum posting guidelines

Not sure where to post? Read the updated guidelines here

### How to use LaTex

Writing equations the easy way

### Study habits of A* students

Top tips from students who have already aced their exams