60.1.531 problem 534

Internal problem ID [10545]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 534
Date solved : Monday, January 27, 2025 at 08:53:35 PM
CAS classification : [[_1st_order, _with_linear_symmetries], _dAlembert]

\begin{align*} 4 x {y^{\prime }}^{3}-6 y {y^{\prime }}^{2}+3 y-x&=0 \end{align*}

✓ Solution by Maple

Time used: 0.098 (sec). Leaf size: 84

dsolve(4*x*diff(y(x),x)^3-6*y(x)*diff(y(x),x)^2+3*y(x)-x=0,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 1.090 (sec). Leaf size: 79

DSolve[-x + 3*y[x] - 6*y[x]*D[y[x],x]^2 + 4*x*D[y[x],x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

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