62.17.4 problem Ex 4

Internal problem ID [12904]
Book : An elementary treatise on differential equations by Abraham Cohen. DC heath publishers. 1906
Section : Chapter IV, differential equations of the first order and higher degree than the first. Article 28. Summary. Page 59
Problem number : Ex 4
Date solved : Tuesday, January 28, 2025 at 04:40:58 AM
CAS classification : [[_homogeneous, `class A`], _rational, _dAlembert]

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

✓ Solution by Maple

Time used: 0.086 (sec). Leaf size: 32

dsolve(3*x*diff(y(x),x)^2-6*y(x)*diff(y(x),x)+x+2*y(x)=0,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*}

✓ Solution by Mathematica

Time used: 0.216 (sec). Leaf size: 67

DSolve[3*x*(D[y[x],x])^2-6*y[x]*D[y[x],x]+x+2*y[x]==0,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*}