60.1.212 problem 216

Internal problem ID [10226]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 216
Date solved : Wednesday, March 05, 2025 at 08:44:34 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y-2 x +1\right ) y^{\prime }+y+x&=0 \end{align*}

✓ Maple. Time used: 0.359 (sec). Leaf size: 61

ode:=(y(x)-2*x+1)*diff(y(x),x)+y(x)+x = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\sqrt {3}\, \tan \left (\operatorname {RootOf}\left (\sqrt {3}\, \ln \left (3\right )-2 \sqrt {3}\, \ln \left (2\right )+\sqrt {3}\, \ln \left (\sec \left (\textit {\_Z} \right )^{2} \left (3 x -1\right )^{2}\right )+2 \sqrt {3}\, c_{1} +6 \textit {\_Z} \right )\right ) \left (-3 x +1\right )}{6}+\frac {x}{2}-\frac {1}{2} \]

✓ Mathematica. Time used: 0.099 (sec). Leaf size: 82

ode=(y[x]-2*x+1)*D[y[x],x]+y[x]+x==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [6 \sqrt {3} \arctan \left (\frac {3 y(x)+1}{\sqrt {3} (-y(x)+2 x-1)}\right )=3 \log \left (\frac {3 x^2+3 y(x)^2-3 (x-1) y(x)-3 x+1}{(1-3 x)^2}\right )+6 \log (3 x-1)+2 c_1,y(x)\right ] \]

✓ Sympy. Time used: 6.302 (sec). Leaf size: 70

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x + (-2*x + y(x) + 1)*Derivative(y(x), x) + y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (x - \frac {1}{3} \right )} = C_{1} - \log {\left (\sqrt {1 - \frac {y{\left (x \right )} + \frac {1}{3}}{x - \frac {1}{3}} + \frac {\left (y{\left (x \right )} + \frac {1}{3}\right )^{2}}{\left (x - \frac {1}{3}\right )^{2}}} \right )} - \sqrt {3} \operatorname {atan}{\left (\frac {\sqrt {3} \left (1 - \frac {2 \left (y{\left (x \right )} + \frac {1}{3}\right )}{x - \frac {1}{3}}\right )}{3} \right )} \]