Internal problem ID [11282]
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]]
\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }=x^{2}-x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)+diff(y(x),x)=x^2-x,y(x), singsol=all)
\[ y \left (x \right ) = \left (-c_{1} x -c_{1} -c_{2} \right ) {\mathrm e}^{-x}+\frac {x^{3}}{3}-\frac {5 x^{2}}{2}+8 x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.243 (sec). Leaf size: 39
DSolve[y'''[x]+2*y''[x]+y'[x]==x^2-x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{6} x \left (2 x^2-15 x+48\right )-e^{-x} (c_2 (x+1)+c_1)+c_3 \]