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Third-order non-homogeneous linear ODE

SByrne55 · 2015-12-28 16:12:17

xy''' + 2y'' = x y(General solution)=Yc + Yp Yc= c1(e^x) + c2 Find the particular solution i.e Yp I've tried finding a series solution and using variation of parameters in conjunction with using the Wronskian (W(x)) in the formula below, but I can't seem to solve it Yp= -Y1*(integral(Y2(x)*x/W(x))dx) +…

28-12-2015 04:12PM

#1

SByrne55

Registered Users, Registered Users 2 Posts: 5 ✭

Join Date: September 2015

Posts: 1

xy''' + 2y'' = x
y(General solution)=Yc + Yp
Yc= c1(e^x) + c2
Find the particular solution i.e Yp
I've tried finding a series solution and using variation of parameters in conjunction with using the Wronskian (W(x)) in the formula below, but I can't seem to solve it

Yp= -Y1*(integral(Y2(x)*x/W(x))dx) + Y2*(integral(Y1(x)*x/W(x))dx)

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Comments

#2 30-12-2015 03:17PM

ride-the-spiral

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Posts: 1247

I think you might be overcomplicating it with the Wronskian approach (which I'm not too sure how to use myself.) Since the lowest derivative that appears is y'', you can let z=y'' and the problem breaks into a first order ODE to solve for z followed by a 2nd order to solve for y''.

0