Internal problem ID [4264]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 35
Problem number: 1042.
ODE order: 1.
ODE degree: 3.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _Clairaut]
\[ \boxed {{y^{\prime }}^{3}-{y^{\prime }}^{2}+x y^{\prime }-y=0} \]
✓ Solution by Maple
Time used: 0.047 (sec). Leaf size: 56
dsolve(diff(y(x),x)^3-diff(y(x),x)^2+x*diff(y(x),x)-y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) &= \frac {x}{3}-\frac {2}{27}-\frac {2 \sqrt {-\left (3 x -1\right )^{3}}}{27} \\ y \left (x \right ) &= \frac {x}{3}-\frac {2}{27}+\frac {2 \sqrt {-\left (3 x -1\right )^{3}}}{27} \\ y \left (x \right ) &= c_{1} \left (c_{1}^{2}-c_{1} +x \right ) \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.025 (sec). Leaf size: 74
DSolve[(y'[x])^3 - (y'[x])^2 +x*y'[x]-y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_1 (x+(-1+c_1) c_1) \\ y(x)\to \frac {1}{27} \left (9 x-2 \left (\sqrt {-(3 x-1)^3}+1\right )\right ) \\ y(x)\to \frac {1}{27} \left (9 x+2 \sqrt {-(3 x-1)^3}-2\right ) \\ \end{align*}