76.2.15 problem 15

Internal problem ID [17351]
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 : 15
Date solved : Tuesday, January 28, 2025 at 10:02:05 AM
CAS classification : [_linear]

\begin{align*} y^{\prime } t +4 y&=t^{2}-t +1 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&={\frac {1}{4}} \end{align*}

✓ Solution by Maple

Time used: 0.023 (sec). Leaf size: 19

dsolve([t*diff(y(t),t)+4*y(t)=t^2-t+1,y(1) = 1/4],y(t), singsol=all)
 

\[ y = \frac {t^{2}}{6}-\frac {t}{5}+\frac {1}{4}+\frac {1}{30 t^{4}} \]

✓ Solution by Mathematica

Time used: 0.049 (sec). Leaf size: 24

DSolve[{t*D[y[t],t]+4*y[t]==t^2-t+1,{y[1]==1/4}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {1}{60} \left (\frac {2}{t^4}+10 t^2-12 t+15\right ) \]