Internal problem ID [5428]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 18. Linear equations with variable coefficients (Equations of second order).
Supplemetary problems. Page 120
Problem number: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-2 y^{\prime } x +2 y=\frac {-x^{2}+1}{x}} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 21
dsolve((1+x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=(1-x^2)/x,y(x), singsol=all)
\[ y = c_{2} x +\left (x^{2}-1\right ) c_{1} +\left (1+\ln \left (x \right )\right ) x \]
✓ Solution by Mathematica
Time used: 0.059 (sec). Leaf size: 27
DSolve[(1+x^2)*y''[x]-2*x*y'[x]+2*y[x]==(1-x^2)/x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x (\log (x)+1)-c_1 (x-i)^2+c_2 x \]