51.3.10 problem 10

Internal problem ID [10353]
Book : First order enumerated odes
Section : section 3. First order odes solved using Laplace method
Problem number : 10
Date solved : Tuesday, September 30, 2025 at 07:22:31 PM
CAS classification : [_linear]

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

Using Laplace method With initial conditions

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

✓ Maple. Time used: 0.125 (sec). Leaf size: 13

ode:=t*diff(y(t),t)+y(t) = t; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(t),method='laplace');
 

\[ y = \frac {t}{2}+\frac {1}{2 t} \]

✓ Mathematica. Time used: 0.017 (sec). Leaf size: 17

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

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

✓ Sympy. Time used: 0.102 (sec). Leaf size: 10

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

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