Internal problem ID [10308]
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]]
Solve \begin {gather*} \boxed {x y^{\prime \prime \prime }-y^{\prime \prime }-y^{\prime } x +y+x^{2}-1=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (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)
\[ y \relax (x ) = x^{2}+3+x c_{1}+c_{2} {\mathrm e}^{x}+c_{3} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.109 (sec). Leaf size: 27
DSolve[x*y'''[x]-y''[x]-x*y'[x]+y[x]==1-x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to x (x+c_1)-c_2 \cosh (x)+i c_3 \sinh (x)+3 \\ \end{align*}