Internal problem ID [7987]
Book: Collection of Kovacic problems
Section: section 1
Problem number: 511.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {\left (x +3\right ) y^{\prime \prime }+\left (2 x +1\right ) y^{\prime }-\left (-x +2\right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve((3+x)*diff(y(x),x$2)+(1+2*x)*diff(y(x),x)-(2-x)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-x} c_{1} +c_{2} {\mathrm e}^{-x} \left (x^{6}+18 x^{5}+135 x^{4}+540 x^{3}+1215 x^{2}+1458 x \right ) \]
✓ Solution by Mathematica
Time used: 0.055 (sec). Leaf size: 29
DSolve[(3+x)*y''[x]+(1+2*x)*y'[x]-(2-x)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} e^{-x-3} \left (c_2 (x+3)^6+6 c_1\right ) \]