88.1.5 problem 19

Internal problem ID [23948]
Book : Elementary Differential Equations. By Lee Roy Wilcox and Herbert J. Curtis. 1961 first edition. International texbook company. Scranton, Penn. USA. CAT number 61-15976
Section : Chapter 1. Introduction. Exercise at page 6
Problem number : 19
Date solved : Thursday, October 02, 2025 at 09:46:43 PM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=\frac {1}{\sqrt {t^{2}+2 t}} \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 17

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

\[ y = \ln \left (1+t +\sqrt {t \left (t +2\right )}\right )+c_1 \]

✓ Mathematica. Time used: 0.047 (sec). Leaf size: 43

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

\begin{align*} y(t)&\to \frac {2 \sqrt {t} \sqrt {t+2} \text {arctanh}\left (\frac {1}{\sqrt {\frac {t}{t+2}}}\right )}{\sqrt {t (t+2)}}+c_1 \end{align*}

✓ Sympy. Time used: 0.208 (sec). Leaf size: 20

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

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