11.7.3 problem 1.2-2 (c)

Internal problem ID [3449]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-2, page 12
Problem number : 1.2-2 (c)
Date solved : Tuesday, September 30, 2025 at 06:38:40 AM
CAS classification : [_linear]

\begin{align*} t y^{\prime }&=y+t^{3} \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.005 (sec). Leaf size: 12

ode:=t*diff(y(t),t) = y(t)+t^3; 
ic:=[y(1) = -2]; 
dsolve([ode,op(ic)],y(t), singsol=all);
 

\[ y = \frac {\left (t^{2}-5\right ) t}{2} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 27

ode=D[y[t],t]==y[t]+t^3; 
ic=y[1]==-2; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to -t^3-3 t^2-6 t+14 e^{t-1}-6 \end{align*}

✓ Sympy. Time used: 0.147 (sec). Leaf size: 12

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t**3 + t*Derivative(y(t), t) - y(t),0) 
ics = {y(1): -2} 
dsolve(ode,func=y(t),ics=ics)
 

\[ y{\left (t \right )} = t \left (\frac {t^{2}}{2} - \frac {5}{2}\right ) \]