10.1.28 problem 28

Internal problem ID [1125]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 28
Date solved : Monday, January 27, 2025 at 04:34:54 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} \frac {2 y}{3}+y^{\prime }&=1-\frac {t}{2} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 15

dsolve(2/3*y(t)+diff(y(t),t) = 1-1/2*t,y(t), singsol=all)
 

\[ y = -\frac {3 t}{4}+\frac {21}{8}+{\mathrm e}^{-\frac {2 t}{3}} c_1 \]

✓ Solution by Mathematica

Time used: 0.065 (sec). Leaf size: 24

DSolve[2/3*y[t]+D[y[t],t] == 1-1/2*t,y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to -\frac {3 t}{4}+c_1 e^{-2 t/3}+\frac {21}{8} \]