Hi everyone,
x^{2}y'-20+x^{2}y^{2}=0; y(1)=1
The question asks me to use substitution
y=1/u*du/dx to solve
So far I have
y'=-1/u^{2}*du/dx+1/u*d^{2}u/dx^{2}
problem is when I sub in for the x^{2}y^{2} term I'm going to get a derivative squared --> y^{2}=(1/u*du/dx)^{2}. Don't know how to resolve this. Please help.
Thank you both I solved this problem BUT I have another one which I am really stuck on this time, supposedly a much easier problem.
There are two questions that I am trying to solve on web assignment. The goal is to find a general form of a particular solution to each ODE. The question asks me to represent all constants in the solution using "P,Q,R,S,T..etc.", in that order.
1. y'''-9y''+14y'=x^{2}
2. y''-9y'+14y=x^{2}e^{4x}
For the first one I wrote:
yp=Px^{3}+Qx^{2}+Rx
Second one:
yp=(Px^{2}+Qx+R)e^{4x}
Neither of the answers are correct, according to the computer. Where did I go wrong?
I am not sure what method you are using to find the particular solutions, but here is one...
We can write the ODE as
Factoring the differential operator we get
So to make the equation equal to zero we act on both sides with
So annihilates
but we must get rid of the part from the complimentary solution (The constant term) so we get
Let me know if this works for you
Thank you very much for you help, but unfortunately that didn't work. I even checked my answer using Wolfram and it seems to be correct, maybe something is wrong with web assignment.
I used the method of undetermined coefficients to find the particular solution.
For Question 1, rewrite your equation as by letting . Then to solve for , the homogeneous solution has complementary function
So the homogeneous solution is .
Now as for the nonhomogeneous solution, use , which means and . Substituting into the DE gives
Therefore the nonhomogeneous solution is , so putting the homogeneous and nonhomogeneous solutions together gives the solution for as