60.1.539 problem 542

Internal problem ID [10553]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 542
Date solved : Monday, January 27, 2025 at 08:56:34 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

\begin{align*} 16 y^{2} {y^{\prime }}^{3}+2 x y^{\prime }-y&=0 \end{align*}

✓ Solution by Maple

Time used: 0.121 (sec). Leaf size: 102

dsolve(16*y(x)^2*diff(y(x),x)^3+2*x*diff(y(x),x)-y(x)=0,y(x), singsol=all)
 

\begin{align*} y &= -\frac {\left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= \frac {\left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= -\frac {i \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= \frac {i \left (-x^{3}\right )^{{1}/{4}} 6^{{1}/{4}}}{3} \\ y &= 0 \\ y &= \sqrt {2}\, \sqrt {c_{1} \left (8 c_{1}^{2}+x \right )} \\ y &= -\sqrt {2}\, \sqrt {c_{1} \left (8 c_{1}^{2}+x \right )} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.112 (sec). Leaf size: 107

DSolve[-y[x] + 2*x*D[y[x],x] + 16*y[x]^2*D[y[x],x]^3==0,y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to \sqrt {c_1 \left (x+2 c_1{}^2\right )} \\ y(x)\to -\frac {\sqrt [4]{-2} x^{3/4}}{3^{3/4}} \\ y(x)\to \frac {(1-i) x^{3/4}}{\sqrt [4]{2} 3^{3/4}} \\ y(x)\to \frac {i \sqrt [4]{-2} x^{3/4}}{3^{3/4}} \\ y(x)\to \frac {\sqrt [4]{-2} x^{3/4}}{3^{3/4}} \\ \end{align*}