Internal problem ID [895]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x y}{x^{2}+1}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 2] \end {align*}
✓ Solution by Maple
Time used: 0.006 (sec). Leaf size: 11
dsolve([diff(y(x),x) - (2*x)/(1+x^2)*y(x)=0,y(0) = 2],y(x), singsol=all)
\[ y \relax (x ) = 2 x^{2}+2 \]
✓ Solution by Mathematica
Time used: 0.03 (sec). Leaf size: 12
DSolve[{y'[x] -(2*x)/(1+x^2)*y[x]==0,y[0]==2},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 2 \left (x^2+1\right ) \\ \end{align*}