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]
\[ \boxed {\left (x^{2}+2\right ) y^{\prime }-4 x \left (y^{2}+2 y+1\right )=0} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 32
dsolve(diff(y(x),x)*(x^2+2)=4*x*(y(x)^2+2*y(x)+1),y(x), singsol=all)
\[ y \left (x \right ) = \frac {-2 \ln \left (x^{2}+2\right )-4 c_{1} -1}{2 \ln \left (x^{2}+2\right )+4 c_{1}} \]
✓ Solution by Mathematica
Time used: 0.195 (sec). Leaf size: 37
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 -\frac {2 \log \left (x^2+2\right )+1+c_1}{2 \log \left (x^2+2\right )+c_1} \\ y(x)\to -1 \\ \end{align*}