60.1.538 problem 541

Internal problem ID [10552]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 541
Date solved : Monday, January 27, 2025 at 08:54:45 PM
CAS classification : [[_1st_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.118 (sec). Leaf size: 95

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

✓ Solution by Mathematica

Time used: 0.115 (sec). Leaf size: 119

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

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