64.7.14 problem 14

Internal problem ID [13317]
Book : Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi. 2004.
Section : Chapter 2, Section 2.4. Special integrating factors and transformations. Exercises page 67
Problem number : 14
Date solved : Monday, March 31, 2025 at 07:51:22 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 4 x +3 y+1+\left (x +y+1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (3\right )&=-4 \end{align*}

✓ Maple. Time used: 0.286 (sec). Leaf size: 34

ode:=4*x+3*y(x)+1+(x+y(x)+1)*diff(y(x),x) = 0; 
ic:=y(3) = -4; 
dsolve([ode,ic],y(x), singsol=all);
 

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

✓ Mathematica. Time used: 0.216 (sec). Leaf size: 165

ode=(4*x+3*y[x]+1)+(x+y[x]+1)*D[y[x],x]==0; 
ic={y[-2]==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _{-2}^{-\frac {(-1)^{2/3} \left (\frac {3 (x-2)}{x+y(x)+1}+2\right )}{\sqrt [3]{2}}}\frac {2}{2 K[1]^3+3 \sqrt [3]{-2} K[1]+2}dK[1]=\frac {1}{9} (-2)^{2/3} \log (x-2)+\frac {1}{9} \left (\frac {1}{2} \left (18 \int _{-2}^{5 (-2)^{2/3}}\frac {2}{2 K[1]^3+3 \sqrt [3]{-2} K[1]+2}dK[1]+2^{2/3} \sqrt {3} \pi +2^{2/3} \log (4)\right )+\frac {1}{2} i \left (2^{2/3} \pi -2^{2/3} \sqrt {3} \log (4)\right )\right ),y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*x + (x + y(x) + 1)*Derivative(y(x), x) + 3*y(x) + 1,0) 
ics = {y(3): -4} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions