Internal problem ID [4117]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 30
Problem number: 881.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, `class A`], _rational, _dAlembert]
\[ \boxed {3 {y^{\prime }}^{2} x -6 y y^{\prime }+2 y=-x} \]
✓ Solution by Maple
Time used: 0.078 (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: 0.314 (sec). Leaf size: 67
DSolve[3 x (y'[x])^2- 6 y[x] y'[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*}