2006-07-30 18:59:30 · 5 answers · asked by marvin_jimenez9 1 in Science & Mathematics ➔ Mathematics
This is a very nice nonlinear equation! :)
Let's differentiate the equation (use the product and chain rules carefully):
2y'y''+2yy'''+2yy'=2y'y''
Subtract 2y'y'' from both sides of the equation
2yy'''+2y''=0
Factor
2y(y'''+y')=0
so y=0 or y'''+y'=0.
The second equation is linear with constant cofficients so its general solution is determined by its characteristic equation:
m^3+m=0
m(m^2+1)=0
m=0 or m= \pm i
which gives us
y=c_1+c_2 cos(t)+c_3 sin(t)
That almost seems like magic... I don't see an obvious error! :)
2006-07-31 02:08:08 · answer #1 · answered by Anonymous · 0⤊ 0⤋
Differential equations at midnight in July... the horror!
2006-07-31 02:18:44 · answer #2 · answered by bogusman82 5 · 0⤊ 0⤋
Try an exponential, e^(ax). Solve for a.
2006-07-31 02:46:16 · answer #3 · answered by Benjamin N 4 · 0⤊ 0⤋
you are asking about metrix orderivative or some thing else
2006-07-31 02:09:01 · answer #4 · answered by sanjeewa 4 · 0⤊ 0⤋
no solution
2006-07-31 02:36:54 · answer #5 · answered by Just ME 2 · 0⤊ 0⤋