36.1 problem 1064

Internal problem ID [3776]

Book: Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section: Various 36
Problem number: 1064.
ODE order: 1.
ODE degree: 3.

CAS Maple gives this as type [[_1st_order, _with_linear_symmetries], _dAlembert]

Solve \begin {gather*} \boxed {8 x \left (y^{\prime }\right )^{3}-12 y \left (y^{\prime }\right )^{2}+9 y=0} \end {gather*}

Solution by Maple

Time used: 0.174 (sec). Leaf size: 80

dsolve(8*x*diff(y(x),x)^3-12*y(x)*diff(y(x),x)^2+9*y(x) = 0,y(x), singsol=all)
 

\begin{align*} y \relax (x ) = -\frac {3 x}{2} \\ y \relax (x ) = \frac {3 x}{2} \\ y \relax (x ) = 0 \\ y \relax (x ) = \frac {x \left (c_{1} \left (3 c_{1}+x \right )\right )^{\frac {3}{2}}}{c_{1}^{3} \left (-\frac {3 \left (3 c_{1}+x \right )}{c_{1}}+9\right )} \\ y \relax (x ) = -\frac {x \left (c_{1} \left (3 c_{1}+x \right )\right )^{\frac {3}{2}}}{c_{1}^{3} \left (-\frac {3 \left (3 c_{1}+x \right )}{c_{1}}+9\right )} \\ \end{align*}

Solution by Mathematica

Time used: 0.163 (sec). Leaf size: 77

DSolve[8 x (y'[x])^3 -12 y[x] (y'[x])^2 + 9 y[x]==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {(x+3 c_1){}^{3/2}}{3 \sqrt {c_1}} \\ y(x)\to \frac {(x+3 c_1){}^{3/2}}{3 \sqrt {c_1}} \\ y(x)\to 0 \\ y(x)\to \text {Indeterminate} \\ y(x)\to -\frac {3 x}{2} \\ y(x)\to \frac {3 x}{2} \\ \end{align*}