75.12.14 problem 288

Internal problem ID [16809]
Book : A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV, G.I. MARKARENKO. MIR, MOSCOW. 1983
Section : Section 12. Miscellaneous problems. Exercises page 93
Problem number : 288
Date solved : Monday, March 31, 2025 at 03:22:19 PM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

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

✓ Maple. Time used: 0.076 (sec). Leaf size: 29

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

\[ y = 2-\frac {\left (x +1\right ) \left (\operatorname {LambertW}\left (-2 c_1 \left (x +1\right )\right )-2\right )}{\operatorname {LambertW}\left (-2 c_1 \left (x +1\right )\right )} \]

✓ Mathematica. Time used: 0.096 (sec). Leaf size: 65

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

\[ \text {Solve}\left [\int _1^{-\frac {2^{2/3} (y(x)-2)}{3 x+y(x)+1}}\frac {1}{K[1]^3-\frac {3 K[1]}{2^{2/3}}+1}dK[1]=\frac {1}{9} 2^{2/3} \log (9 (x+1))+c_1,y(x)\right ] \]

✓ Sympy. Time used: 1.016 (sec). Leaf size: 19

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

\[ y{\left (x \right )} = - x + e^{C_{1} + W\left (2 \left (x + 1\right ) e^{- C_{1}}\right )} + 1 \]