85.30.3 problem 3

Internal problem ID [22619]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter two. First order and simple higher order ordinary differential equations. A Exercises at page 63
Problem number : 3
Date solved : Thursday, October 02, 2025 at 08:55:10 PM
CAS classification : [_Clairaut]

\begin{align*} y&=x y^{\prime }-\tan \left (y^{\prime }\right ) \end{align*}

✓ Maple. Time used: 0.066 (sec). Leaf size: 63

ode:=y(x) = x*diff(y(x),x)-tan(diff(y(x),x)); 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= -\sqrt {x}\, \sqrt {1-\frac {1}{x}}+x \,\operatorname {arcsec}\left (\sqrt {x}\right ) \\ y &= \sqrt {x}\, \sqrt {1-\frac {1}{x}}+\pi x -x \,\operatorname {arcsec}\left (\sqrt {x}\right ) \\ y &= c_1 x -\tan \left (c_1 \right ) \\ \end{align*}

✓ Mathematica. Time used: 0.237 (sec). Leaf size: 25

ode=y[x]==x*D[y[x],{x,1}]-Tan[ D[y[x],{x,1}] ]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to c_1 x-\tan (c_1)\\ y(x)&\to 0\\ y(x)&\to \text {Indeterminate} \end{align*}

✗ Sympy

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

NotImplementedError : multiple generators [_X0, tan(_X0)] 
No algorithms are implemented to solve equ