Internal problem ID [13520]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 42.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {x y^{\prime \prime }-y^{\prime }+3 x {y^{\prime }}^{3}=0} \]
✓ Solution by Maple
Time used: 0.032 (sec). Leaf size: 42
dsolve(x*diff(y(x),x$2)-diff(y(x),x)=-3*x* diff(y(x),x)^3,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \int \frac {x}{\sqrt {2 x^{3}-c_{1}}}d x +c_{2} y \left (x \right ) = \int -\frac {x}{\sqrt {2 x^{3}-c_{1}}}d x +c_{2} \end{align*}
✓ Solution by Mathematica
Time used: 1.949 (sec). Leaf size: 195
DSolve[x*y''[x]-y'[x]==-3*x* (y'[x])^3,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to c_2-\frac {x^2 \sqrt {1+\frac {2 x^3}{c_1}} \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {2}{3},\frac {5}{3},-\frac {2 x^3}{c_1}\right )}{2 \sqrt {2 x^3+c_1}} y(x)\to \frac {x^2 \sqrt {1+\frac {2 x^3}{c_1}} \operatorname {Hypergeometric2F1}\left (\frac {1}{2},\frac {2}{3},\frac {5}{3},-\frac {2 x^3}{c_1}\right )}{2 \sqrt {2 x^3+c_1}}+c_2 y(x)\to c_2 y(x)\to -\frac {3 \sqrt {x^3} \operatorname {Gamma}\left (\frac {5}{3}\right )}{\sqrt {2} x \operatorname {Gamma}\left (\frac {2}{3}\right )}+c_2 y(x)\to \frac {3 \sqrt {x^3} \operatorname {Gamma}\left (\frac {5}{3}\right )}{\sqrt {2} x \operatorname {Gamma}\left (\frac {2}{3}\right )}+c_2 \end{align*}