60.1.532 problem 535

Internal problem ID [10546]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 535
Date solved : Monday, January 27, 2025 at 08:53:36 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: 0.069 (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 &= -\frac {3 x}{2} \\ y &= \frac {3 x}{2} \\ y &= 0 \\ y &= -\frac {\left (3 c_{1} +x \right ) \sqrt {c_{1} \left (3 c_{1} +x \right )}}{3 c_{1}} \\ y &= \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: 0.336 (sec). Leaf size: 77

DSolve[9*y[x] - 12*y[x]*D[y[x],x]^2 + 8*x*D[y[x],x]^3==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*}