00:01
In this question we are given the equation y double dash plus y is equal to 2 times square x.
00:09
So we have to find the general solution using variation of pattern.
00:13
First let's write the cf, it's the complementary function.
00:18
So the above equation can be written as the auxiliary equation which is m squared plus m is equal to 0.
00:31
So now factorizing it we will be getting m is equal to plus or minus i.
00:38
So our cf is going to be p1 cos x plus p2 sin x.
00:46
So now let's take the wronskian for the same.
00:50
So y1 of x is going to be cos x and let's take our y2 of x is equal to sin x.
01:01
Taking the wronskian w is equal to y1 y2 y1 dash y2 dash.
01:11
So let's substitute the values we will be having cos x, sin x.
01:16
Differentiation of cos x is going to be minus sin x and sin x is going to be cos x.
01:23
So solving this we will be getting w is equal to cos square x plus sin square x...