Internal problem ID [2627]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth
edition, 2015
Section: Chapter 1, First-Order Differential Equations. Section 1.4, Separable Differential
Equations. page 43
Problem number: Problem 6.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-\frac {2 x \left (y-1\right )}{x^{2}+3}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(diff(y(x),x)=(2*x*(y(x)-1))/(x^2+3),y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{2}+3 c_{1} +1 \]
✓ Solution by Mathematica
Time used: 0.031 (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*}