11.7.6 problem 1.2-2 (f)

Internal problem ID [3452]
Book : Ordinary Differential Equations, Robert H. Martin, 1983
Section : Problem 1.2-2, page 12
Problem number : 1.2-2 (f)
Date solved : Tuesday, September 30, 2025 at 06:38:45 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: 14

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

\[ y = \frac {t^{4}+7}{4 t} \]

✓ Mathematica. Time used: 0.036 (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+4 e^{1-t}-6 \end{align*}

✓ Sympy. Time used: 0.112 (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)
 

\[ y{\left (t \right )} = \frac {\frac {t^{4}}{4} + \frac {7}{4}}{t} \]