Internal problem ID [10268]
Book: An elementary treatise on differential equations by Abraham Cohen. DC heath publishers.
1906
Section: Chapter VII, Linear differential equations with constant coefficients. Article 52. Summary.
Page 117
Problem number: Ex 8.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }-x^{2}+x=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)+diff(y(x),x)=x^2-x,y(x), singsol=all)
\[ y \relax (x ) = \frac {x^{3}}{3}-{\mathrm e}^{-x} c_{2}+c_{1} \left (-{\mathrm e}^{-x} x -{\mathrm e}^{-x}\right )-\frac {5 x^{2}}{2}+8 x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.041 (sec). Leaf size: 38
DSolve[y'''[x]+2*y''[x]+y'[x]==x^2-x,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} x (x (2 x-15)+48)-e^{-x} (c_2 (x+1)+c_1)+c_3 \\ \end{align*}