20.2.6 problem Problem 6

Internal problem ID [3598]
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
Date solved : Monday, January 27, 2025 at 07:47:06 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {2 x \left (y-1\right )}{x^{2}+3} \end{align*}

✓ Solution by Maple

Time used: 0.001 (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: 0.033 (sec). Leaf size: 20

DSolve[D[y[x],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*}