Internal problem ID [10244]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 48. Page
103
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 {y^{\prime \prime \prime }-3 y^{\prime \prime }-y^{\prime }+3 y-x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 30
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)-diff(y(x),x)+3*y(x)=x^2,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{2}}{3}+\frac {2 x}{9}+\frac {20}{27}+c_{1} {\mathrm e}^{x}+c_{2} {\mathrm e}^{-x}+c_{3} {\mathrm e}^{3 x} \]
✓ Solution by Mathematica
Time used: 0.005 (sec). Leaf size: 41
DSolve[y'''[x]-3*y''[x]-y'[x]+3*y[x]==x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{9} x (3 x+2)+c_1 e^{-x}+c_2 e^x+c_3 e^{3 x}+\frac {20}{27} \\ \end{align*}