5.34, §2 Solution

y' + x² y = x²

The equation is linear.

Solution of the homogeneous equation:

Solution of the inhomogeneous equation:

into

y' + x² y = x²

Solution:

Note: function y(x)=1 is called a particular solution. It is one solution that satisfies the inhomogeneous equation.

The general solution of linear equations is always: (any arbitrary particular solution) plus (the general solution of the homogeneous equation).

(What is wrong in the graph above)?