Internal problem ID [4205]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 972.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _rational]
\[ \boxed {y^{2} {y^{\prime }}^{2}-3 x y^{\prime }+y=0} \]
✓ Solution by Maple
Time used: 0.094 (sec). Leaf size: 124
dsolve(y(x)^2*diff(y(x),x)^2-3*x*diff(y(x),x)+y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {18^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{2} y \left (x \right ) = -\frac {18^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, 18^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4} y \left (x \right ) = -\frac {18^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, 18^{\frac {1}{3}} \left (x^{2}\right )^{\frac {1}{3}}}{4} y \left (x \right ) = 0 y \left (x \right ) = \operatorname {RootOf}\left (-\ln \left (x \right )+\int _{}^{\textit {\_Z}}-\frac {3 \left (4 \textit {\_a}^{3}-3 \sqrt {-4 \textit {\_a}^{3}+9}-9\right )}{2 \textit {\_a} \left (4 \textit {\_a}^{3}-9\right )}d \textit {\_a} +c_{1} \right ) x^{\frac {2}{3}} \end{align*}
✓ Solution by Mathematica
Time used: 0.623 (sec). Leaf size: 247
DSolve[y[x]^2 (y'[x])^2-3 x y'[x]+y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to e^{\frac {c_1}{3}} \sqrt [3]{e^{c_1}-3 i x} y(x)\to -\sqrt [3]{-1} e^{\frac {c_1}{3}} \sqrt [3]{e^{c_1}-3 i x} y(x)\to (-1)^{2/3} e^{\frac {c_1}{3}} \sqrt [3]{e^{c_1}-3 i x} y(x)\to e^{\frac {c_1}{3}} \sqrt [3]{3 i x+e^{c_1}} y(x)\to -\sqrt [3]{-1} e^{\frac {c_1}{3}} \sqrt [3]{3 i x+e^{c_1}} y(x)\to (-1)^{2/3} e^{\frac {c_1}{3}} \sqrt [3]{3 i x+e^{c_1}} y(x)\to 0 y(x)\to \left (-\frac {3}{2}\right )^{2/3} x^{2/3} y(x)\to \left (\frac {3}{2}\right )^{2/3} x^{2/3} y(x)\to -\sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} x^{2/3} \end{align*}