4.1.20 problem 20

Internal problem ID [1117]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 20
Date solved : Tuesday, September 30, 2025 at 04:22:16 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 17

ode:=(t+1)*y(t)+t*diff(y(t),t) = t; 
ic:=[y(ln(2)) = 1]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

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

✓ Mathematica. Time used: 0.023 (sec). Leaf size: 23

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

\begin{align*} y(t)&\to \frac {e^{-t} \left (e^t (t-1)+2\right )}{t} \end{align*}

✓ Sympy. Time used: 0.209 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(t*Derivative(y(t), t) - t + (t + 1)*y(t),0) 
ics = {y(log(2)): 1} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = 1 - \frac {1}{t} + \frac {2 e^{- t}}{t} \]