60.1.210 problem 214

Internal problem ID [10224]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 214
Date solved : Sunday, March 30, 2025 at 03:32:33 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} \left (y+x -1\right ) y^{\prime }-y+2 x +3&=0 \end{align*}

✓ Maple. Time used: 0.174 (sec). Leaf size: 51

ode:=(-1+x+y(x))*diff(y(x),x)-y(x)+2*x+3 = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {5}{3}+\frac {\tan \left (\operatorname {RootOf}\left (\sqrt {2}\, \ln \left (\left (3 x +2\right )^{2} \sec \left (\textit {\_Z} \right )^{2}\right )+\sqrt {2}\, \ln \left (2\right )+2 \sqrt {2}\, c_1 -2 \textit {\_Z} \right )\right ) \sqrt {2}\, \left (-3 x -2\right )}{3} \]

✓ Mathematica. Time used: 0.106 (sec). Leaf size: 78

ode=(y[x]+x-1)*D[y[x],x]-y[x]+2*x+3==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [2 \sqrt {2} \arctan \left (\frac {-y(x)+2 x+3}{\sqrt {2} (y(x)+x-1)}\right )=2 \log \left (\frac {6 x^2+3 y(x)^2-10 y(x)+8 x+11}{(3 x+2)^2}\right )+4 \log (3 x+2)+3 c_1,y(x)\right ] \]

✓ Sympy. Time used: 4.260 (sec). Leaf size: 56

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(2*x + (x + y(x) - 1)*Derivative(y(x), x) - y(x) + 3,0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ \log {\left (x + \frac {2}{3} \right )} = C_{1} - \log {\left (\sqrt {2 + \frac {\left (y{\left (x \right )} - \frac {5}{3}\right )^{2}}{\left (x + \frac {2}{3}\right )^{2}}} \right )} - \frac {\sqrt {2} \operatorname {atan}{\left (\frac {\sqrt {2} \left (y{\left (x \right )} - \frac {5}{3}\right )}{2 \left (x + \frac {2}{3}\right )} \right )}}{2} \]