12.9.44 problem 39 part(b)

Internal problem ID [1800]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 5 linear second order equations. Section 5.6 Reduction or order. Page 253
Problem number : 39 part(b)
Date solved : Monday, January 27, 2025 at 05:35:09 AM
CAS classification : [[_homogeneous, `class C`], _Riccati]

\begin{align*} y^{\prime }+y^{2}+4 y x +4 x^{2}+2&=0 \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 23

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

\[ y = \frac {-2 c_1 x +2 x^{2}-1}{-x +c_1} \]

✓ Solution by Mathematica

Time used: 0.132 (sec). Leaf size: 22

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

\begin{align*} y(x)\to -2 x+\frac {1}{x+c_1} \\ y(x)\to -2 x \\ \end{align*}