10.1.22 problem 22

Internal problem ID [1119]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 22
Date solved : Monday, January 27, 2025 at 04:34:04 AM
CAS classification : [[_linear, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.011 (sec). Leaf size: 19

dsolve([-y(t)+2*diff(y(t),t) = exp(1/3*t),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: 0.056 (sec). Leaf size: 26

DSolve[{-y[t]+2*D[y[t],t] == Exp[1/3*t],y[0]==a},y[t],t,IncludeSingularSolutions -> True]
 

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