60.1.219 problem 220

Internal problem ID [10233]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 220
Date solved : Monday, January 27, 2025 at 06:40:40 PM
CAS classification : [_rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 43

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

\begin{align*} y &= \sqrt {{\mathrm e}^{\frac {x^{2}}{2}} c_{1} -x^{2}-2} \\ y &= -\sqrt {{\mathrm e}^{\frac {x^{2}}{2}} c_{1} -x^{2}-2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 7.559 (sec). Leaf size: 57

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

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