Internal problem ID [943]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 2, First order equations. separable equations. Section 2.2 Page 52
Problem number: 17.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime } \left (x^{2}+2\right )-4 x \left (y^{2}+2 y+1\right )=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 31
dsolve(diff(y(x),x)*(x^2+2)=4*x*(y(x)^2+2*y(x)+1),y(x), singsol=all)
\[ y \relax (x ) = -\frac {2 \ln \left (x^{2}+2\right )+4 c_{1}+1}{2 \left (\ln \left (x^{2}+2\right )+2 c_{1}\right )} \]
✓ Solution by Mathematica
Time used: 0.209 (sec). Leaf size: 27
DSolve[y'[x]*(x^2+2)==4*x*(y[x]^2+2*y[x]+1),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -1-\frac {1}{2 \log \left (x^2+2\right )+c_1} \\ y(x)\to -1 \\ \end{align*}