60.1.206 problem 207

Internal problem ID [10220]
Book : Differential Gleichungen, E. Kamke, 3rd ed. Chelsea Pub. NY, 1948
Section : Chapter 1, linear first order
Problem number : 207
Date solved : Monday, January 27, 2025 at 06:39:44 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

\begin{align*} y^{\prime } y+y^{2}+4 x \left (1+x \right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 37

dsolve(y(x)*diff(y(x),x)+y(x)^2+4*x*(x+1)=0,y(x), singsol=all)
 

\begin{align*} y &= \sqrt {c_{1} {\mathrm e}^{-2 x}-4 x^{2}} \\ y &= -\sqrt {c_{1} {\mathrm e}^{-2 x}-4 x^{2}} \\ \end{align*}

✓ Solution by Mathematica

Time used: 5.987 (sec). Leaf size: 47

DSolve[y[x]*D[y[x],x]+y[x]^2+4*x*(x+1)==0,y[x],x,IncludeSingularSolutions -> True]
 

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