85.26.4 problem 4

Internal problem ID [22592]
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. C Exercises at page 57
Problem number : 4
Date solved : Sunday, October 12, 2025 at 05:53:16 AM
CAS classification : [`y=_G(x,y')`]

\begin{align*} x^{2}+y \left (x -y\right )^{2} \tan \left (\frac {y}{x}\right )-\left (x^{2}+x \left (x -y\right )^{2} \tan \left (\frac {y}{x}\right )\right ) y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.123 (sec). Leaf size: 36

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

\begin{align*} y &= x \\ y &= \operatorname {RootOf}\left (\cos \left (\textit {\_Z} \right )-{\mathrm e}^{\frac {c_1 \textit {\_Z} x -c_1 x -1}{x \left (\textit {\_Z} -1\right )}}\right ) x \\ \end{align*}

✓ Mathematica. Time used: 1.547 (sec). Leaf size: 25

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

\[ \text {Solve}\left [\frac {1}{x-y(x)}-\log \left (\cos \left (\frac {y(x)}{x}\right )\right )=c_1,y(x)\right ] \]

✗ Sympy

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

Timed Out