Internal problem ID [7313]
Book: Own collection of miscellaneous problems
Section: section 5.0
Problem number: 20.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (1+x \right ) y=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 14
dsolve(x*diff(y(x),x$2)-(2*x+1)*diff(y(x),x)+(x+1)*y(x)=0,y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{x} \left (c_{2} x^{2}+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.023 (sec). Leaf size: 23
DSolve[x*y''[x]-(2*x+1)*y'[x]+(x+1)*y[x]==0,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^x \left (c_2 x^2+2 c_1\right ) \]