29.36.1 problem 1064

Internal problem ID [5628]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 36
Problem number : 1064
Date solved : Monday, January 27, 2025 at 12:32:02 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 8 x {y^{\prime }}^{3}-12 y {y^{\prime }}^{2}+9 y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.231 (sec). Leaf size: 61

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 \left (x \right ) &= -\frac {3 x}{2} \\ y \left (x \right ) &= \frac {3 x}{2} \\ y \left (x \right ) &= 0 \\ y \left (x \right ) &= -\frac {\left (3 c_{1} +x \right ) \sqrt {c_{1} \left (3 c_{1} +x \right )}}{3 c_{1}} \\ y \left (x \right ) &= \frac {\left (3 c_{1} +x \right ) \sqrt {c_{1} \left (3 c_{1} +x \right )}}{3 c_{1}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.339 (sec). Leaf size: 77

DSolve[8 x (D[y[x],x])^3 -12 y[x] (D[y[x],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*}