Internal problem ID [11848]
Book: Differential Equations by Shepley L. Ross. Third edition. John Willey. New Delhi.
2004.
Section: Chapter 4, Section 4.4. Variation of parameters. Exercises page 162
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (1+x \right )^{2} y^{\prime \prime }-2 \left (1+x \right ) y^{\prime }+2 y=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve((x+1)^2*diff(y(x),x$2)-2*(x+1)*diff(y(x),x)+2*y(x)=1,y(x), singsol=all)
\[ y \left (x \right ) = \left (1+x \right )^{2} c_{1} +c_{2} x +c_{2} +\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.032 (sec). Leaf size: 23
DSolve[(x+1)^2*y''[x]-2*(x+1)*y'[x]+2*y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_2 (x+1)^2+c_1 (x+1)+\frac {1}{2} \]