00:01
Hello everyone, in this problem we need to find the particular explicit particular solution for the given initial value problem.
00:08
So we are given with this differential value sorry differential equation and with the initial value.
00:14
So now from the given differential equation we can take the value of p to be minus 2 by x and q to be x cube cos x.
00:32
Now integrating factor i f will be equal to e power integral of p dx.
00:41
P is minus 2 by x dx.
00:47
So integrating here simplifying we get the value to be x to the power minus.
00:54
So now we can write the general solution which will be y multiplied by the integrating factor to be equal to integral of integrating factor multiplied by q dx plus c.
01:11
So this is the general solution format for the given differential equation.
01:18
So now substituting the corresponding values y multiplied by x to the power minus 2 to be equals to integral of x power minus 2 multiplied by q is x cube cos of x plus c sorry dx.
01:37
So simplifying this we get this to be y multiplied by x to the power minus 2 to be equals to integral of x cos x dx plus c.
01:53
So now integrating this by using integration by parts so we get y multiplied by x to the power minus 2 to be equal to x sin x minus integral of sin x multiplied by 1 dx plus c...