Internal problem ID [4206]
Book: Ordinary differential equations and their solutions. By George Moseley Murphy.
1960
Section: Various 33
Problem number: 973.
ODE order: 1.
ODE degree: 2.
CAS Maple gives this as type [[_1st_order, _with_linear_symmetries]]
\[ \boxed {y^{2} {y^{\prime }}^{2}-6 x^{3} y^{\prime }+4 x^{2} y=0} \]
✓ Solution by Maple
Time used: 0.11 (sec). Leaf size: 118
dsolve(y(x)^2*diff(y(x),x)^2-6*x^3*diff(y(x),x)+4*x^2*y(x) = 0,y(x), singsol=all)
\begin{align*} y \left (x \right ) = \frac {18^{\frac {1}{3}} x^{\frac {4}{3}}}{2} y \left (x \right ) = \left (-\frac {18^{\frac {1}{3}} x^{\frac {1}{3}}}{4}-\frac {i \sqrt {3}\, 18^{\frac {1}{3}} x^{\frac {1}{3}}}{4}\right ) x y \left (x \right ) = \left (-\frac {18^{\frac {1}{3}} x^{\frac {1}{3}}}{4}+\frac {i \sqrt {3}\, 18^{\frac {1}{3}} x^{\frac {1}{3}}}{4}\right ) x 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 )}{4 \textit {\_a} \left (4 \textit {\_a}^{3}-9\right )}d \textit {\_a} +c_{1} \right ) x^{\frac {4}{3}} \end{align*}
✓ Solution by Mathematica
Time used: 2.556 (sec). Leaf size: 304
DSolve[y[x]^2 (y'[x])^2-6 x^3 y'[x]+4 x^2 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} \text {Solve}\left [\frac {\sqrt {9 x^6-4 x^2 y(x)^3} \log \left (\sqrt {9 x^4-4 y(x)^3}+3 x^2\right )}{2 x \sqrt {9 x^4-4 y(x)^3}}-\frac {3}{4} \left (\frac {\sqrt {9 x^6-4 x^2 y(x)^3} \log (y(x))}{x \sqrt {9 x^4-4 y(x)^3}}-\log (y(x))\right )=c_1,y(x)\right ] \text {Solve}\left [\frac {3}{4} \left (\frac {\sqrt {9 x^6-4 x^2 y(x)^3} \log (y(x))}{x \sqrt {9 x^4-4 y(x)^3}}+\log (y(x))\right )-\frac {\sqrt {9 x^6-4 x^2 y(x)^3} \log \left (\sqrt {9 x^4-4 y(x)^3}+3 x^2\right )}{2 x \sqrt {9 x^4-4 y(x)^3}}=c_1,y(x)\right ] y(x)\to \left (-\frac {3}{2}\right )^{2/3} x^{4/3} y(x)\to \left (\frac {3}{2}\right )^{2/3} x^{4/3} y(x)\to -\sqrt [3]{-1} \left (\frac {3}{2}\right )^{2/3} x^{4/3} \end{align*}