10.6.9 problem 9

Internal problem ID [1226]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 9
Date solved : Monday, January 27, 2025 at 04:45:59 AM
CAS classification : [_rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} y^{\prime }&=\frac {-1-2 y x}{x^{2}+2 y} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 47

dsolve(diff(y(x),x) = (-1-2*x*y(x))/(x^2+2*y(x)),y(x), singsol=all)
 

\begin{align*} y &= -\frac {x^{2}}{2}-\frac {\sqrt {x^{4}-4 c_1 -4 x}}{2} \\ y &= -\frac {x^{2}}{2}+\frac {\sqrt {x^{4}-4 c_1 -4 x}}{2} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.128 (sec). Leaf size: 61

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

\begin{align*} y(x)\to \frac {1}{2} \left (-x^2-\sqrt {x^4-4 x+4 c_1}\right ) \\ y(x)\to \frac {1}{2} \left (-x^2+\sqrt {x^4-4 x+4 c_1}\right ) \\ \end{align*}