Answer: In each of 10 through 15, verify that the given functions y1 and y2 satisfy the

Chapter 3, Problem 11

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QUESTION:

In each of 10 through 15, verify that the given functions y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. In 14 and 15, g is an arbitrary continuous function. t2 y__ t (t + 2) y_ + (t + 2) y = 2t3, t > 0; y1(t) = t, y2(t) = tet

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QUESTION:

In each of 10 through 15, verify that the given functions y1 and y2 satisfy the corresponding homogeneous equation; then find a particular solution of the given nonhomogeneous equation. In 14 and 15, g is an arbitrary continuous function. t2 y__ t (t + 2) y_ + (t + 2) y = 2t3, t > 0; y1(t) = t, y2(t) = tet

ANSWER:

Step 1 of 3

Given:  ,

Consider the equation  which is equivalent to

And

Now check if  and  satisfies the homogeneous equation or not. Now calculate the derivatives of  and  as:

,  ,  ,

Now put all the above derivatives in equation .

Thus, the values of and  satisfies the equation.

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