Find the complementary solution of [itex]y^\left(4\right) + 2y'' + y = sint[/itex](adsbygoogle = window.adsbygoogle || []).push({});

Homogeneous Form would be [itex]y^\left(4\right) + 2y'' + y = 0[/itex]

[itex]r^4 + 2r^2 + r = 0 \rightarrow r(r^3 + 2r + 1) = 0[/itex]

This is where I'm stuck. Once I find [itex]y_c(t)[/itex] I should be able to finish the problem, but I'm having trouble at this step. What would be the next step here?

The book's solution is [itex]y_c(t) = C_1 cost + C_2 sint + C_3 tcost + C_4 tsint[/itex] which would suggest complex numbers involved here.

Edit: Found my error, it was in the r equation.

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# 4th Order Variation of Parameters

Loading...

**Physics Forums | Science Articles, Homework Help, Discussion**