00:01
Problem we are going to solve the following differential equation.
00:04
Y double prime plus y equal to second of x.
00:09
So we have this inhomogeneous equation with not so elementary function on the right hand side.
00:17
So let us use or let us try the method of variation of parameters to obtain the particular solution and then we will be able to write down the most channel solution.
00:29
Okay, now as always, we start with the complementary solution, namely the solution to the corresponding homogeneous equation.
00:42
So we have this differential equation with constant coefficients, then we can replace the derivative terms by this parameter d.
00:51
So we obtain d equal to plus or minus i.
00:55
And noting that the solutions go like exponential dx, we have.
01:02
We have the first fundamental solution given as cosine x and the second one is sine x.
01:13
Okay, now let us obtain the particular solution using the method of variation of parameters...