Internal problem ID [14275]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number: 53.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [[_linear, `class A`]]
\[ \boxed {y^{\prime }-\frac {y}{2}=5 \cos \left (t \right )+2 \,{\mathrm e}^{t}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 23
dsolve(diff(y(t),t)-1/2*y(t)=5*cos(t)+2*exp(t),y(t), singsol=all)
\[ y \left (t \right ) = 4 \sin \left (t \right )-2 \cos \left (t \right )+4 \,{\mathrm e}^{t}+{\mathrm e}^{\frac {t}{2}} c_{1} \]
✓ Solution by Mathematica
Time used: 0.124 (sec). Leaf size: 28
DSolve[y'[t]-1/2*y[t]==5*Cos[t]+2*Exp[t],y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to 4 \left (e^t+\sin (t)\right )-2 \cos (t)+c_1 e^{t/2} \]