Internal problem ID [5328]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 9. Equations of first order and higher degree. Supplemetary problems. Page
65
Problem number: 22.
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: 0.14 (sec). Leaf size: 126
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 {2^{\frac {1}{3}} \left (-x^{2}\right )^{\frac {1}{3}} \left (3 i 3^{\frac {1}{6}}+3^{\frac {2}{3}}\right )}{4} \\ y \left (x \right ) &= \frac {2^{\frac {1}{3}} \left (-x^{2}\right )^{\frac {1}{3}} \left (-3^{\frac {2}{3}}+3 i 3^{\frac {1}{6}}\right )}{4} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= \operatorname {RootOf}\left (-2 \ln \left (x \right )+3 \left (\int _{}^{\textit {\_Z}}-\frac {4 \textit {\_a}^{3}-3 \sqrt {4 \textit {\_a}^{3}+9}+9}{\textit {\_a} \left (4 \textit {\_a}^{3}+9\right )}d \textit {\_a} \right )+2 c_{1} \right ) x^{\frac {2}{3}} \\ \end{align*}
✓ Solution by Mathematica
Time used: 0.574 (sec). Leaf size: 239
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]{-3 x+e^{c_1}} \\ y(x)\to -\sqrt [3]{-1} e^{\frac {c_1}{3}} \sqrt [3]{-3 x+e^{c_1}} \\ y(x)\to (-1)^{2/3} e^{\frac {c_1}{3}} \sqrt [3]{-3 x+e^{c_1}} \\ y(x)\to e^{\frac {c_1}{3}} \sqrt [3]{3 x+e^{c_1}} \\ y(x)\to -\sqrt [3]{-1} e^{\frac {c_1}{3}} \sqrt [3]{3 x+e^{c_1}} \\ y(x)\to (-1)^{2/3} e^{\frac {c_1}{3}} \sqrt [3]{3 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 \frac {\sqrt [3]{-1} 3^{2/3} x^{2/3}}{2^{2/3}} \\ \end{align*}