12.6.29 problem 38

Internal problem ID [1708]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Exact equations. Section 2.5 Page 79
Problem number : 38
Date solved : Monday, January 27, 2025 at 05:31:17 AM
CAS classification : [_rational, [_Abel, `2nd type`, `class B`]]

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

With initial conditions

\begin{align*} y \left (1\right )&=-2 \end{align*}

✓ Solution by Maple

Time used: 0.012 (sec). Leaf size: 15

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

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

✓ Solution by Mathematica

Time used: 0.702 (sec). Leaf size: 38

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

\[ y(x)\to \frac {1}{2} \left (-\frac {1}{x^2}-\frac {\sqrt {x^3 \left (x^2+1\right )^2}}{x^{7/2}}-1\right ) \]