Internal problem ID [3567]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 29
Problem number: 836.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_homogeneous, class G]]
Solve \begin {gather*} \boxed {3 \left (y^{\prime }\right )^{2}+4 y^{\prime } x +x^{2}-y=0} \end {gather*}
✓ Solution by Maple
Time used: 0.188 (sec). Leaf size: 111
dsolve(3*diff(y(x),x)^2+4*x*diff(y(x),x)+x^2-y(x) = 0,y(x), singsol=all)
\begin{align*} y \relax (x ) = -\frac {x^{2}}{3} \\ y \relax (x ) = -\frac {5 x^{2}}{12}-\frac {x \left (-x -\sqrt {3}\, c_{1}\right )}{6}+\frac {c_{1}^{2}}{4} \\ y \relax (x ) = -\frac {5 x^{2}}{12}-\frac {x \left (-x +\sqrt {3}\, c_{1}\right )}{6}+\frac {c_{1}^{2}}{4} \\ y \relax (x ) = -\frac {5 x^{2}}{12}+\frac {x \left (x -\sqrt {3}\, c_{1}\right )}{6}+\frac {c_{1}^{2}}{4} \\ y \relax (x ) = -\frac {5 x^{2}}{12}+\frac {x \left (x +\sqrt {3}\, c_{1}\right )}{6}+\frac {c_{1}^{2}}{4} \\ \end{align*}
✓ Solution by Mathematica
Time used: 2.123 (sec). Leaf size: 79
DSolve[3 (y'[x])^2+4 x y'[x]+x^2-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{12} \left (-3 x-1+e^{c_1}\right ) \left (x-1+e^{c_1}\right ) \\ y(x)\to \frac {1}{12} \left (-x+1+e^{c_1}\right ) \left (3 x+1+e^{c_1}\right ) \\ y(x)\to -\frac {x^2}{3} \\ y(x)\to \frac {1}{12} ((2-3 x) x+1) \\ \end{align*}