Internal problem ID [13522]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 44.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _exact, _linear, _nonhomogeneous]]
\[ \boxed {x^{2} y^{\prime \prime }+x y^{\prime }-y=\frac {1}{x^{2}+1}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(x^2*diff(y(x),x$2)+x*diff(y(x),x)-y(x)=1/(1+x^2),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1}}{x}+c_{2} x -\frac {\arctan \left (x \right ) x^{2}+\arctan \left (x \right )+x}{2 x} \]
✓ Solution by Mathematica
Time used: 0.031 (sec). Leaf size: 33
DSolve[x^2*y''[x]+x*y'[x]-y[x]==1/(1+x^2),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^2 \arctan (x)+\arctan (x)-2 c_2 x^2+x-2 c_1}{2 x} \]