Internal problem ID [11290]
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]]
\[ \boxed {x y^{\prime \prime }-\left (2 x +1\right ) y^{\prime }+y \left (1+x \right )=x^{2}-x -1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 16
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)
\[ y \left (x \right ) = \left (c_{1} x^{2}+c_{2} \right ) {\mathrm e}^{x}+x \]
✓ Solution by Mathematica
Time used: 0.275 (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]
\[ y(x)\to \frac {1}{2} c_2 e^x x^2+x+c_1 e^x \]