Up: 5.38 Previous: 5.38, §1 Asked

5.38, §2 Solution

xy' + y = x y3

It is a Bernoulli equation since it has terms linear in y and a power of y.

x y-3 y' + y-2 = x

Put u=y-2:

Solution of the homogeneous equation:

Solution of the inhomogeneous equation:

u = C(x) x2

into the inhomogeneous equation:

Solution:

For C0=0 :

For x=-2/C0, y is infinite.

For C0<0:

For C0>0:

Total:


Up: 5.38 Previous: 5.38, §1 Asked