Internal problem ID [2040]
Book: Differential equations and linear algebra, Stephen W. Goode, second edition, 2000
Section: 1.4, page 36
Problem number: 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
Solve \begin {gather*} \boxed {y^{\prime }-\frac {2 x \left (y-1\right )}{x^{2}+3}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.002 (sec). Leaf size: 13
dsolve(diff(y(x),x)=(2*x*(y(x)-1))/(x^2+3),y(x), singsol=all)
\[ y \relax (x ) = 1+\left (x^{2}+3\right ) c_{1} \]
✓ Solution by Mathematica
Time used: 0.033 (sec). Leaf size: 20
DSolve[y'[x]==(2*x*(y[x]-1))/(x^2+3),y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to 1+c_1 \left (x^2+3\right ) \\ y(x)\to 1 \\ \end{align*}