I don"t think that"s right, however I"m not certain what else to do. And also where to go from there.  We have to use the initial values for the general solution\$\$y=c_1sin x+c_2cos x+y_p\$\$the details solution is\$\$y_p=Axsin x+Bxcos x\$\$\$\$A=0,B=frac12\$\$so the general solution is\$\$y=c_1sin x+c_2cos x+fracx2cos x\$\$now you can use the initial values to find the \$A\$ and also \$B\$ \$y"" + y = -sin x\$

solve the homogeneous equation

\$y = c_1 sin t + c_2 cos x + y_p\$

Undetermined coefficients.

You are watching: Y'+y=sinx

\$y = A xsin x + Bxcos x\$

Why \$A x sin x + B xcos x,\$ and also not the more simple-minded \$A sin x + B cos x\$?

\$A sin x + B cos x\$ is already component of the homogeneous solution. So, when we plug it into the diff eq, that is going to "go away." We need something that when distinguished (twice) has actually a component that amounts to \$-sin x\$ yet is not in the homogeneous solution.

\$y" = Asin x + Bcos x - B xsin x + Axcos x\y"" = -2B sin x + 2Acos x - A xsin x + Bxcos x\ y""+y = -2B sin x + 2Acos x = -sin x\B = frac 12, A = 0\$

\$y = c_1 sin t + c_2 cos x + frac 12 x cos x\y(0) = C_2 = 0\y"(0) = C_1 = 0\$

\$y = frac 12 xcos x\$

re-publishing
point out
monitor
edited Oct 18 "16 at 20:05
answered Oct 18 "16 in ~ 18:42 Doug MDoug M
\$endgroup\$
1
include a comment |

Thanks because that contributing solution to tastecraftedmcd.comematics Stack Exchange!

But avoid

Asking for help, clarification, or responding to various other answers.Making statements based upon opinion; ago them increase with references or an individual experience.

Use tastecraftedmcd.comJax to style equations. tastecraftedmcd.comJax reference.

To find out more, check out our tips on writing good answers.

Draft saved

send

### Post together a guest

name
email Required, however never shown

### Post together a guest

surname
email

Required, however never shown

## Not the price you're spring for? Browse other questions tagged ordinary-differential-equations or questioning your very own question.

The Overflow Blog
Featured ~ above Meta
related
9
exactly how to usage the Fredholm alternate in an ODE
1
assist with a differential equation?
1
fixing the differential equation \$y'' + y = 8cos(x) cos(2x)\$
0
just how to obtain from imaginary index number of e to real sine and also cosine?
1
resolving this Differential Equation (second order,non-homogeneous)
0
question reguarding early value problem ODE
1
present that if \$y\$ is a nontrivial equipment of \$y''+y=0\$, then either \$y(0) eq 0\$ or \$y′(0) eq 0\$
0
general solution of \$tx''-x'+4t^3x=4t^3\$
hot Network inquiries an ext hot inquiries

concern feed tastecraftedmcd.com
company
stack Exchange Network
site style / logo design © 2022 stack Exchange Inc; user contributions license is granted under cc by-sa. Rev2021.12.22.41046

tastecraftedmcd.comematics ridge Exchange works best with JavaScript permitted her privacy

By click “Accept all cookies”, girlfriend agree ridge Exchange have the right to store cookies on your machine and disclose details in accordance v our Cookie Policy.