29.17.4 problem 463

Internal problem ID [5061]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 463
Date solved : Tuesday, March 04, 2025 at 07:49:45 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.021 (sec). Leaf size: 22

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

\[ y \left (x \right ) = \tan \left (\operatorname {RootOf}\left (\ln \left (\sec \left (\textit {\_Z} \right )^{2}\right )+\textit {\_Z} +2 \ln \left (x \right )+2 c_{1} \right )\right ) x \]

✓ Mathematica. Time used: 0.035 (sec). Leaf size: 30

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

\[ \text {Solve}\left [\arctan \left (\frac {y(x)}{x}\right )+\log \left (\frac {y(x)^2}{x^2}+1\right )=-2 \log (x)+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.020 (sec). Leaf size: 27

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

\[ \log {\left (x \right )} = C_{1} - \log {\left (\sqrt {1 + \frac {y^{2}{\left (x \right )}}{x^{2}}} \right )} - \frac {\operatorname {atan}{\left (\frac {y{\left (x \right )}}{x} \right )}}{2} \]