Internal problem ID [10276]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VIII, Linear differential equations of the second order. Article 53. Change of
dependent variable. Page 125
Problem number: Ex 2.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
Solve \begin {gather*} \boxed {x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+\left (x +1\right ) y-x^{2}+x +1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(x*diff(y(x),x$2)-(2*x+1)*diff(y(x),x)+(x+1)*y(x)=x^2-x-1,y(x), singsol=all)
\[ y \relax (x ) = {\mathrm e}^{x} c_{2}+x^{2} {\mathrm e}^{x} c_{1}+x \]
✓ Solution by Mathematica
Time used: 0.072 (sec). Leaf size: 25
DSolve[x*y''[x]-(2*x+1)*y'[x]+(x+1)*y[x]==x^2-x-1,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} c_2 e^x x^2+x+c_1 e^x \\ \end{align*}