76.2.28 problem 28

Internal problem ID [17364]
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 : 28
Date solved : Tuesday, January 28, 2025 at 10:03:07 AM
CAS classification : [[_linear, `class A`]]

\begin{align*} y^{\prime }+\frac {4 y}{3}&=1-\frac {t}{4} \end{align*}

With initial conditions

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

✓ Solution by Maple

Time used: 0.014 (sec). Leaf size: 21

dsolve([diff(y(t),t)+4/3*y(t)=1-1/4*t,y(0) = y__0],y(t), singsol=all)
 

\[ y = -\frac {3 t}{16}+\frac {57}{64}+{\mathrm e}^{-\frac {4 t}{3}} y_{0} -\frac {57 \,{\mathrm e}^{-\frac {4 t}{3}}}{64} \]

✓ Solution by Mathematica

Time used: 0.084 (sec). Leaf size: 38

DSolve[{D[y[t],t]+4/3*y[t]==1-1/4*t,{y[0]==y0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to e^{-4 t/3} \left (\int _0^t-\frac {1}{4} e^{\frac {4 K[1]}{3}} (K[1]-4)dK[1]+\text {y0}\right ) \]