66.7.15 problem 15

Internal problem ID [16043]
Book : DIFFERENTIAL EQUATIONS by Paul Blanchard, Robert L. Devaney, Glen R. Hall. 4th edition. Brooks/Cole. Boston, USA. 2012
Section : Chapter 1. First-Order Differential Equations. Exercises section 1.9 page 133
Problem number : 15
Date solved : Thursday, October 02, 2025 at 10:39:35 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }&=\frac {y}{t^{2}}+4 \cos \left (t \right ) \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 24

ode:=diff(y(t),t) = y(t)/t^2+4*cos(t); 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (4 \int \cos \left (t \right ) {\mathrm e}^{\frac {1}{t}}d t +c_1 \right ) {\mathrm e}^{-\frac {1}{t}} \]

✓ Mathematica. Time used: 0.041 (sec). Leaf size: 34

ode=D[y[t],t]==y[t]/t^2+4*Cos[t]; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to e^{-1/t} \left (\int _1^t4 e^{\frac {1}{K[1]}} \cos (K[1])dK[1]+c_1\right ) \end{align*}

✓ Sympy. Time used: 9.939 (sec). Leaf size: 27

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-4*cos(t) + Derivative(y(t), t) - y(t)/t**2,0) 
ics = {} 
dsolve(ode,func=y(t),ics=ics)
 

\[ - 4 \int e^{\frac {1}{t}} \cos {\left (t \right )}\, dt - \int \frac {y{\left (t \right )} e^{\frac {1}{t}}}{t^{2}}\, dt = C_{1} \]