Internal problem ID [11573]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 1, Differential equations and their solutions. Exercises page 13
Problem number: 1(d).
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _homogeneous]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }+4 y^{\prime } x +2 y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve((1+x^2)*diff(y(x),x$2)+4*x*diff(y(x),x)+2*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} x +c_{2}}{x^{2}+1} \]
✓ Solution by Mathematica
Time used: 0.039 (sec). Leaf size: 20
DSolve[(1+x^2)*y''[x]+4*x*y'[x]+2*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {c_2 x+c_1}{x^2+1} \]