57.1.29 problem 29

Internal problem ID [9013]
Book : First order enumerated odes
Section : section 1
Problem number : 29
Date solved : Wednesday, March 05, 2025 at 07:14:37 AM
CAS classification : [_Riccati]

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

✗ Maple

ode:=diff(y(x),x) = cos(x)+y(x)^2/x; 
dsolve(ode,y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

ode=D[y[x],x]==Cos[x]+y[x]^2/x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

Not solved

✗ Sympy

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

NotImplementedError : The given ODE -cos(x) + Derivative(y(x), x) - y(x)**2/x cannot be solved by the lie group method