12.2.9 problem 9

Internal problem ID [1545]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 2, First order equations. Linear first order. Section 2.1 Page 41
Problem number : 9
Date solved : Monday, January 27, 2025 at 04:59:32 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }-\frac {2 x y}{x^{2}+1}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 11

dsolve([diff(y(x),x) - (2*x)/(1+x^2)*y(x)=0,y(0) = 2],y(x), singsol=all)
 

\[ y = 2 x^{2}+2 \]

✓ Solution by Mathematica

Time used: 0.027 (sec). Leaf size: 12

DSolve[{D[y[x],x] -(2*x)/(1+x^2)*y[x]==0,y[0]==2},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to 2 \left (x^2+1\right ) \]