76.2.22 problem 22

Internal problem ID [17358]
Book : Differential equations. An introduction to modern methods and applications. James Brannan, William E. Boyce. Third edition. Wiley 2015
Section : Chapter 2. First order differential equations. Section 2.2 (Linear equations: Method of integrating factors). Problems at page 54
Problem number : 22
Date solved : Tuesday, January 28, 2025 at 10:02:19 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

\begin{align*} y \left (0\right )&=a \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 19

dsolve([2*diff(y(t),t)-y(t)=exp(t/3),y(0) = a],y(t), singsol=all)
 

\[ y = {\mathrm e}^{\frac {t}{3}} \left (-3+\left (a +3\right ) {\mathrm e}^{\frac {t}{6}}\right ) \]

✓ Solution by Mathematica

Time used: 0.060 (sec). Leaf size: 26

DSolve[{2*D[y[t],t]-y[t]==Exp[t/3],{y[0]==a}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{t/3} \left ((a+3) e^{t/6}-3\right ) \]