10.6.5 problem 5

Internal problem ID [1222]
Book : Elementary differential equations and boundary value problems, 10th ed., Boyce and DiPrima
Section : Miscellaneous problems, end of chapter 2. Page 133
Problem number : 5
Date solved : Monday, January 27, 2025 at 04:45:51 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 59

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

\begin{align*} y &= \frac {-x^{2}+\sqrt {x \left (x^{3}-4 c_1 -4 x \right )}}{2 x} \\ y &= \frac {-x^{2}-\sqrt {x \left (x^{3}-4 c_1 -4 x \right )}}{2 x} \\ \end{align*}

✓ Solution by Mathematica

Time used: 0.512 (sec). Leaf size: 67

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

\begin{align*} y(x)\to -\frac {x^2+\sqrt {x \left (x^3-4 x+4 c_1\right )}}{2 x} \\ y(x)\to \frac {-x^2+\sqrt {x \left (x^3-4 x+4 c_1\right )}}{2 x} \\ \end{align*}