00:01
In this problem, we have a differential equation y, cosine x, dx plus y plus 2, sine x, d .y is equal to 0.
00:18
We need to calculate the integrating factor to make this differential equation exact.
00:26
So first of all, let's compare the given equation with equation mdx plus n d y is equal to 0 so by the comparison we get m is equal to y cosine x and n is equals to y plus 2 sine x now let's differentiate m with respect to y so we can write del m over del y is equals to cosine x similarly let's differentiate n with respect to x, so we get del n over del x is equals to y plus 2 times cosine x.
01:23
Now we can observe that del m over del y is not equals to del n over del x.
01:37
Hence, we can conclude that given equation is not an exact equation.
01:53
Now, let's find the value of del n over del x minus del m over del y.
02:05
So this is equals to y plus 2 times cosine x minus cosine x.
02:18
On further simplifying, we get y plus 1 times cosine x...