A community for students. Sign up today!
Here's the question you clicked on:
 0 viewing
 2 years ago
\[y_P(x)=Ax^2+Bx+C\]
\[y'_P=2Ax+B\]
\[y''_P=2A\]
\[ay''+by'+cy=Gx\]
\[2A+(2Ax+B)2(Ax^2+Bx+C)=x^2\]
I understand all of the above except the \[...=x^2\] part.
Why is G(x)=x^2?
 2 years ago
\[y_P(x)=Ax^2+Bx+C\] \[y'_P=2Ax+B\] \[y''_P=2A\] \[ay''+by'+cy=Gx\] \[2A+(2Ax+B)2(Ax^2+Bx+C)=x^2\] I understand all of the above except the \[...=x^2\] part. Why is G(x)=x^2?

This Question is Closed

across
 2 years ago
Best ResponseYou've already chosen the best response.1You're just posting the particular solution to the ODE. Can you post the ODE itself so that we can give it a better look? I mean, you obtained some strange coefficients I didn't see until you decided to operate on the derivatives linearly.

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1oh I'm sorry I left one part out \[y''+y'2y=x^2\] soo sorry....I guess I'm just tired, cant read my calc book =P

MathSofiya
 2 years ago
Best ResponseYou've already chosen the best response.1I have another question, which I'll probably figure out as soon as I post it :) I understand that: 2A=1 but why is: 2Ax+B=0 and Ax^2+Bx+C=0? should't they equal 1 as well?

across
 2 years ago
Best ResponseYou've already chosen the best response.1You're looking at the solution process incorrectly. Let \(y''+y'2y=x^2\). Since this is an inhomogeneous ODE with source term \(x^2\), the particular solution is assumed to have the form \(y_p=Ax^2+Bx+C\). Differentiating as you did\[\begin{align}y_p'&=2Ax+B\\y_p''&=2A\end{align}\]and combining linearly yields\[\begin{align}(2A)+(2Ax+B)2(Ax^2+Bx+C)&=x^2\\2A+2Ax+B2Ax^22Bx2C&=x^2\\(2A)x^2+(2A2B)x+(2A+B2C)&=(1)x^2+(0)x+(0)\end{align}\]Observe that the \(2A\) term on the LHS corresponds to the \(x^2\) on the RHS, while the \(2A2B\) and \(2A+B2C\) terms both correspond to \(0\). Hence, this implies that \(2A=1\). I'm sure you can wrap the rest up from here.
Ask your own question
Ask a QuestionFind more explanations on OpenStudy
Your question is ready. Sign up for free to start getting answers.
spraguer
(Moderator)
5
→ View Detailed Profile
is replying to Can someone tell me what button the professor is hitting...
23
 Teamwork 19 Teammate
 Problem Solving 19 Hero
 Engagement 19 Mad Hatter
 You have blocked this person.
 ✔ You're a fan Checking fan status...
Thanks for being so helpful in mathematics. If you are getting quality help, make sure you spread the word about OpenStudy.