Question

Given y1=t² and y2=t⁻¹ satisfy the corresponding homogeneous equation of then the general solution to the non-homogeneous equation can be written as _______. Use variation of parameters to find _______.

Answer 1

The general solution to the non-homogeneous equation can be written as y(t) = A*t^2 + B*(1/t), and the particular solution can be found using the variation of parameters method.

Step-by-step explanation:

The general solution to the non-homogeneous equation can be written as y(t) = A*t^2 + B*(1/t), where A and B are constants.

To find the particular solution using the variation of parameters method, we need to find the two particular solutions y1p and y2p. We substitute y1 = t^2 and y2 = 1/t into the homogeneous equation to get two linearly independent solutions. Then we can find the Wronskian W(t) and the functions u1(t) and u2(t). Finally, we can find the particular solution y(t) = u1(t)*y1 + u2(t)*y2.

In summary, the general solution to the non-homogeneous equation is y(t) = A*t^2 + B*(1/t), and the particular solution can be found using the variation of parameters method.