74.5.46 problem 53

Internal problem ID [16010]
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
Date solved : Tuesday, January 28, 2025 at 08:26:24 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }-\frac {y}{2}&=5 \cos \left (t \right )+2 \,{\mathrm e}^{t} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 23

dsolve(diff(y(t),t)-1/2*y(t)=5*cos(t)+2*exp(t),y(t), singsol=all)
 

\[ y = -2 \cos \left (t \right )+4 \sin \left (t \right )+4 \,{\mathrm e}^{t}+{\mathrm e}^{\frac {t}{2}} c_{1} \]

✓ Solution by Mathematica

Time used: 0.117 (sec). Leaf size: 44

DSolve[D[y[t],t]-1/2*y[t]==5*Cos[t]+2*Exp[t],y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{t/2} \left (\int _1^te^{-\frac {K[1]}{2}} \left (5 \cos (K[1])+2 e^{K[1]}\right )dK[1]+c_1\right ) \]