My apologies, I will make sure to do that.

I can't help but think the answer generated by Maple seems quite "complicted", as opposed to the y = 2*t - sin(t) + cos(t), suggested by my textbook.

I used the ODE analyser and had it generate the maple command used:

sol1 := dsolve([`@@`(D,2)(y)(t)+D(y)(t) = 2*t, y(1/4*Pi) = 1/2*Pi, D(y)(1/4*Pi) = 2-2^(1/2)], {y(t)}, method = laplace);

The result output was:

2:      y(t) = t^2+(1/2)*exp(-t)*(-8+2*sqrt(2)+Pi)/exp(-(1/4)*Pi)-2*t+(1/2)*Pi-(1/16)*Pi^2+4-sqrt(2)

Is the only way to get from equation #2 to  y = 2*t - sin(t) + cos(t) by hand?

My apologies, I will make sure to do that.

I can't help but think the answer generated by Maple seems quite "complicted", as opposed to the y = 2*t - sin(t) + cos(t), suggested by my textbook.

I used the ODE analyser and had it generate the maple command used:

sol1 := dsolve([`@@`(D,2)(y)(t)+D(y)(t) = 2*t, y(1/4*Pi) = 1/2*Pi, D(y)(1/4*Pi) = 2-2^(1/2)], {y(t)}, method = laplace);

The result output was:

2:      y(t) = t^2+(1/2)*exp(-t)*(-8+2*sqrt(2)+Pi)/exp(-(1/4)*Pi)-2*t+(1/2)*Pi-(1/16)*Pi^2+4-sqrt(2)

Is the only way to get from equation #2 to  y = 2*t - sin(t) + cos(t) by hand?

By the way, according to my textbook, the result is supposed to be:
y = 2*t - sin(t) + cos(t)