Internal problem ID [11332]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter IX, Miscellaneous methods for solving equations of higher order than first.
Article 59. Linear equations with particular integral known. Page 136
Problem number: Ex 2.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _with_linear_symmetries]]
\[ \boxed {x y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime } x +y=-x^{2}+1} \]
✓ Solution by Maple
Time used: 0.031 (sec). Leaf size: 22
dsolve(x*diff(y(x),x$3)-diff(y(x),x$2)-x*diff(y(x),x)+y(x)=1-x^2,y(x), singsol=all)
\[ y \left (x \right ) = x^{2}+3+x c_{1} +c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.242 (sec). Leaf size: 28
DSolve[x*y'''[x]-y''[x]-x*y'[x]+y[x]==1-x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2+c_1 x-c_2 \cosh (x)+i c_3 \sinh (x)+3 \]