60.1.537 problem 540

Internal problem ID [10551]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 540
Date solved : Monday, January 27, 2025 at 08:54:41 PM
CAS classification : [_quadrature]

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

✓ Solution by Maple

Time used: 0.060 (sec). Leaf size: 111

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

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

✓ Solution by Mathematica

Time used: 3.466 (sec). Leaf size: 61

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

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