74.7.55 problem 60

Internal problem ID [16053]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.5, page 64
Problem number : 60
Date solved : Thursday, March 13, 2025 at 07:37:00 AM
CAS classification : [_linear]

\begin{align*} y&=t \left (y^{\prime }+1\right )+2 y^{\prime }+1 \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 21

ode:=y(t) = t*(diff(y(t),t)+1)+2*diff(y(t),t)+1; 
dsolve(ode,y(t), singsol=all);
 

\[ y = \left (-t -2\right ) \ln \left (t +2\right )-1+\left (t +2\right ) c_{1} \]

✓ Mathematica. Time used: 0.039 (sec). Leaf size: 25

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

\[ y(t)\to t-(t+2) \log (t+2)+c_1 t+1+2 c_1 \]

✓ Sympy. Time used: 0.258 (sec). Leaf size: 24

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

\[ y{\left (t \right )} = C_{1} t + 2 C_{1} - t \log {\left (t + 2 \right )} - 2 \log {\left (t + 2 \right )} - 1 \]