# Thread: u and v are solutions

1. ## u and v are solutions

Clearly u = cos x and v = sin x are solutions of y'' + y = 0. Show that $z = u^2$ and z = uv are solutions of z''' + 4z' = 0

I dont understand how to start this off. Im not asking for the answer just trying to understand what is going on or what to do.

2. Is what's meant to be clear, clear? Just in case a picture helps...

... differentiating downwards.

Spoiler:

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Don't integrate - balloontegrate!

Balloon Calculus; standard integrals, derivatives and methods

Balloon Calculus Drawing with LaTeX and Asymptote!

3. Originally Posted by onemore
Clearly u = cos x and v = sin x are solutions of y'' + y = 0. Show that $z = u^2$ and z = uv are solutions of z''' + 4z' = 0

I dont understand how to start this off. Im not asking for the answer just trying to understand what is going on or what to do.
$z= u^2= cos^2(x)$. What is $(cos^2(x))'''+ 4(cos^2(x))'$?

$z= uv= cos(x)sin(x)$. What is $(cos(x)sin(x))'''+ 4(cos(x)sin(x))'$?