0. We will solve it using methods similar to thosefor a Cauchy-Euler ODE, and variation of parameters. (If you can think of another way of solvingthis ODE and want to check your answer you may of...

Extracted text: 5. Consider the ODE tx' +2x = t, for t > 0. We will solve it using methods similar to those for a Cauchy-Euler ODE, and variation of parameters. (If you can think of another way of solving this ODE and want to check your answer you may of course do so, but what we want to see here is your answers to the questions below.) (a) First, we will find the homogeneous solution xh to the homogeneous ODE. Find the value of = ctm. What can you say about the values that the constant c can take on? (b) Now, we will find a particular solution xp to the inhomogeneous ODE. To do this, assume u(t) is a function of t and m is the value you found above. Find a m such that xh utm, where u Xp function u(t) such that x, is a particular solution of the ODE. (c) Give the general solution of the ODE. No need to explain.