/sci/ - Science & Math

>>11539365
Write down the auxiliary equation to get the homogeneous solution: [math] y_h=k_1e^{-2t}+k_2e^{2t}+k_3 [/math]. For the particular solution, I just guessed that it had a form of [math] y_p=At^4+Bt^3+Ct^2+Dt+F\sin t+Gte^{-2t} [/math] (don't worry about the constant term, it will just get absorbed into k3 anyway). Now you just compute the third derivative of the particular solution form, subtract four times the first derivative, and solve for the variables by looking at the RHS of the ODE. You should get [math] y_p=-(1/8)t^2-(3/5)\sin t+(1/8)te^{-2t} [/math]. Finally, [math] y=y_h+y_p [/math].
>>11539875
I didn't recognize the name, but I looked him up and I've seen a couple videos before. There isn't any reason I can imagine that they aren't okay.