20.3.5 problem Problem 5

Internal problem ID [3614]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 1, First-Order Differential Equations. Section 1.6, First-Order Linear Differential Equations. page 59
Problem number : Problem 5
Date solved : Monday, January 27, 2025 at 07:47:38 AM
CAS classification : [_linear]

\begin{align*} y^{\prime }+\frac {2 x y}{-x^{2}+1}&=4 x \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 24

dsolve(diff(y(x),x)+2*x/(1-x^2)*y(x)=4*x,y(x), singsol=all)
 

\[ y \left (x \right ) = \left (2 \ln \left (x -1\right )+2 \ln \left (x +1\right )+c_{1} \right ) \left (x^{2}-1\right ) \]

✓ Solution by Mathematica

Time used: 0.033 (sec). Leaf size: 22

DSolve[D[y[x],x]+2*x/(1-x^2)*y[x]==4*x,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x^2-1\right ) \left (2 \log \left (x^2-1\right )+c_1\right ) \]