Internal problem ID [5413]
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: 22.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x^{2}+1\right ) y^{\prime \prime }-2 x y^{\prime }+2 y=2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve((1+x^2)*diff(y(x),x$2)-2*x*diff(y(x),x)+2*y(x)=2,y(x), singsol=all)
\[ y \left (x \right ) = c_{1} x^{2}+c_{2} x -c_{1} +1 \]
✓ Solution by Mathematica
Time used: 0.043 (sec). Leaf size: 22
DSolve[(1+x^2)*y''[x]-2*x*y'[x]+2*y[x]==2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -c_1 (x-i)^2+c_2 x+1 \]