60.1.502 problem 505

Internal problem ID [10516]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 505
Date solved : Monday, January 27, 2025 at 08:42:13 PM
CAS classification : [_separable]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 52

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

\begin{align*} y &= \sqrt {x^{2}+c_{1}} \\ y &= -\sqrt {x^{2}+c_{1}} \\ y &= \sqrt {c_{1} x^{2}+1}\, x \\ y &= -\sqrt {c_{1} x^{2}+1}\, x \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.675 (sec). Leaf size: 85

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

\begin{align*} y(x)\to -\sqrt {x^2+2 c_1} \\ y(x)\to \sqrt {x^2+2 c_1} \\ y(x)\to -\sqrt {x^2+c_1 x^4} \\ y(x)\to \sqrt {x^2+c_1 x^4} \\ y(x)\to -x \\ y(x)\to x \\ \end{align*}