15.8.35 problem 37

Internal problem ID [3038]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 12, page 46
Problem number : 37
Date solved : Sunday, March 30, 2025 at 01:13:12 AM
CAS classification : [[_homogeneous, `class C`], _rational, [_Abel, `2nd type`, `class C`], _dAlembert]

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

✓ Maple. Time used: 0.171 (sec). Leaf size: 52

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

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

✓ Mathematica. Time used: 0.121 (sec). Leaf size: 78

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

\[ \text {Solve}\left [2 \sqrt {2} \arctan \left (\frac {-3 y(x)+x-2}{\sqrt {2} (3 y(x)+2 x+2)}\right )=2 \log \left (\frac {3 x^2+9 y(x)^2+6 (x+2) y(x)+4 x+4}{3 x^2}\right )+4 \log (x)+3 c_1,y(x)\right ] \]

✓ Sympy. Time used: 2.290 (sec). Leaf size: 61

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

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