90.5.7 problem 7

Internal problem ID [25126]
Book : Ordinary Differential Equations. By William Adkins and Mark G Davidson. Springer. NY. 2010. ISBN 978-1-4614-3617-1
Section : Chapter 1. First order differential equations. Exercises at page 71
Problem number : 7
Date solved : Thursday, October 02, 2025 at 11:52:46 PM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Maple. Time used: 0.023 (sec). Leaf size: 27

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

\[ -\arctan \left (\frac {y}{\sqrt {t^{2}-y^{2}}}\right )+\ln \left (t \right )-c_1 = 0 \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -sqrt(t**2 - y(t)**2) - y(t) + Derivative(y(t), t) cannot be sol