29.17.1 problem 460

Internal problem ID [5058]
Book : Ordinary differential equations and their solutions. By George Moseley Murphy. 1960
Section : Various 17
Problem number : 460
Date solved : Monday, January 27, 2025 at 10:06:59 AM
CAS classification : [[_homogeneous, `class D`], _rational, _Bernoulli]

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

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 37

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

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

✓ Solution by Mathematica

Time used: 6.066 (sec). Leaf size: 47

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

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