4.1.15 problem 15

Internal problem ID [1112]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Section 2.1. Page 40
Problem number : 15
Date solved : Tuesday, September 30, 2025 at 04:22:08 AM
CAS classification : [_linear]

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

With initial conditions

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

✓ Maple. Time used: 0.024 (sec). Leaf size: 19

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

\[ y = \frac {t^{2}}{4}-\frac {t}{3}+\frac {1}{2}+\frac {1}{12 t^{2}} \]

✓ Mathematica. Time used: 0.019 (sec). Leaf size: 22

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

\begin{align*} y(t)&\to \frac {1}{12} \left (3 t^2+\frac {1}{t^2}-4 t+6\right ) \end{align*}

✓ Sympy. Time used: 0.148 (sec). Leaf size: 20

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

\[ y{\left (t \right )} = \frac {t^{2}}{4} - \frac {t}{3} + \frac {1}{2} + \frac {1}{12 t^{2}} \]