68.7.26 problem 26

Internal problem ID [17390]
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 : 26
Date solved : Thursday, October 02, 2025 at 02:16:11 PM
CAS classification : [[_homogeneous, `class A`], _dAlembert]

\begin{align*} y+2 \sqrt {t^{2}+y^{2}}-t y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 26

ode:=y(t)+2*(t^2+y(t)^2)^(1/2)-t*diff(y(t),t) = 0; 
dsolve(ode,y(t), singsol=all);
 

\[ \frac {-c_1 \,t^{3}+y+\sqrt {t^{2}+y^{2}}}{t^{3}} = 0 \]

✓ Mathematica. Time used: 0.133 (sec). Leaf size: 15

ode=(y[t]+2*Sqrt[t^2+y[t]^2])-(t)*D[y[t],t]==0; 
ic={}; 
DSolve[{ode,ic},y[t],t,IncludeSingularSolutions->True]
 

\begin{align*} y(t)&\to t \sinh (2 \log (t)+c_1) \end{align*}

✓ Sympy. Time used: 0.915 (sec). Leaf size: 14

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

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