83.23.14 problem 14

Internal problem ID [19295]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter V. Singular solutions. Exercise V at page 76
Problem number : 14
Date solved : Tuesday, January 28, 2025 at 01:24:37 PM
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: 0.038 (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 \left (x \right ) &= x \\ y \left (x \right ) &= -\frac {x}{3} \\ y \left (x \right ) &= \frac {4 c_{1}^{2}+2 c_{1} x +x^{2}}{6 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.271 (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*}