76.2.20 problem 20

Internal problem ID [17356]
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 : 20
Date solved : Tuesday, January 28, 2025 at 10:02:15 AM
CAS classification : [_linear]

\begin{align*} y^{\prime } t +\left (1+t \right ) y&=t \end{align*}

With initial conditions

\begin{align*} y \left (\ln \left (2\right )\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 17

dsolve([t*diff(y(t),t)+(1+t)*y(t)=t,y(ln(2)) = 1],y(t), singsol=all)
 

\[ y = \frac {2 \,{\mathrm e}^{-t}+t -1}{t} \]

✓ Solution by Mathematica

Time used: 0.063 (sec). Leaf size: 56

DSolve[{t*D[y[t],t]+(1+t)*y[t]==t,{y[Log[2]]==1}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \frac {e^{-t-1} \left (\int _1^te^{K[1]+1} K[1]dK[1]-\int _1^{\log (2)}e^{K[1]+1} K[1]dK[1]+e \log (4)\right )}{t} \]