29.30.21 problem 881

Internal problem ID [5461]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 30
Problem number : 881
Date solved : Sunday, March 30, 2025 at 08:14:15 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

\begin{align*} 3 x {y^{\prime }}^{2}-6 y y^{\prime }+x +2 y&=0 \end{align*}

✓ Maple. Time used: 0.041 (sec). Leaf size: 32

ode:=3*x*diff(y(x),x)^2-6*y(x)*diff(y(x),x)+x+2*y(x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\begin{align*} y &= x \\ y &= -\frac {x}{3} \\ y &= \frac {4 c_1^{2}+2 c_1 x +x^{2}}{6 c_1} \\ \end{align*}

✓ Mathematica. Time used: 0.24 (sec). Leaf size: 67

ode=3 x (D[y[x],x])^2- 6 y[x] D[y[x],x]+x +2 y[x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)\to \frac {1}{3} x \left (1+2 \cosh \left (-\log (x)+\sqrt {3} c_1\right )\right ) \\ y(x)\to \frac {1}{3} x \left (1+2 \cosh \left (\log (x)+\sqrt {3} c_1\right )\right ) \\ y(x)\to -\frac {x}{3} \\ y(x)\to x \\ \end{align*}

✓ Sympy. Time used: 3.949 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x*Derivative(y(x), x)**2 + x - 6*y(x)*Derivative(y(x), x) + 2*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {4 x^{2} e^{- C_{1}}}{3} + \frac {x}{3} + \frac {e^{C_{1}}}{12} \]