35.2 problem Ex 2

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*}