29.15.15 problem 423

Internal problem ID [5021]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 15
Problem number : 423
Date solved : Monday, January 27, 2025 at 10:03:57 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 6.146 (sec). Leaf size: 47

DSolve[y[x] D[y[x],x]+4(1+x)x+y[x]^2==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*}