12.3.16 problem 17

Internal problem ID [1593]
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
Date solved : Monday, January 27, 2025 at 05:12:45 AM
CAS classification : [_separable]

\begin{align*} y^{\prime } \left (x^{2}+2\right )&=4 x \left (y^{2}+2 y+1\right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (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)
 

\[ y = \frac {-2 \ln \left (x^{2}+2\right )-4 c_1 -1}{2 \ln \left (x^{2}+2\right )+4 c_1} \]

✓ Solution by Mathematica

Time used: 0.207 (sec). Leaf size: 37

DSolve[D[y[x],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*}