25.1.9 problem 9

Internal problem ID [4221]
Book : Advanced Mathematica, Book2, Perkin and Perkin, 1992
Section : Chapter 11.3, page 316
Problem number : 9
Date solved : Monday, January 27, 2025 at 08:42:47 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {4 x y}{x^{2}+1} \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 13

dsolve(diff(y(x),x)=(4*x*y(x))/(x^2+1),y(x), singsol=all)
 

\[ y \left (x \right ) = c_{1} \left (x^{2}+1\right )^{2} \]

✓ Solution by Mathematica

Time used: 0.030 (sec). Leaf size: 20

DSolve[D[y[x],x]==(4*x*y[x])/(x^2+1),y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to c_1 \left (x^2+1\right )^2 \\ y(x)\to 0 \\ \end{align*}