15.5.17 problem 21

Internal problem ID [2953]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 9, page 38
Problem number : 21
Date solved : Monday, January 27, 2025 at 07:00:26 AM
CAS classification : [_separable]

\begin{align*} y \left (x^{2}-1\right )+x \left (x^{2}+1\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=2 \end{align*}

✓ Solution by Maple

Time used: 0.009 (sec). Leaf size: 14

dsolve([y(x)*(x^2-1)+x*(x^2+1)*diff(y(x),x)=0,y(1) = 2],y(x), singsol=all)
 

\[ y = \frac {4 x}{x^{2}+1} \]

✓ Solution by Mathematica

Time used: 0.046 (sec). Leaf size: 15

DSolve[{y[x]*(x^2-1)+x*(x^2+1)*D[y[x],x]==0,{y[1]==2}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {4 x}{x^2+1} \]