Internal problem ID [2219]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _with_linear_symmetries]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-2 y=x^{2}-8} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 26
dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=x^2-8,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{2 x}+{\mathrm e}^{-x} c_{1} -\frac {x^{2}}{2}+\frac {x}{2}+\frac {13}{4} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 36
DSolve[y''[x]-y'[x]-2*y[x]==x^2-8,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{4} \left (-2 x^2+2 x+13\right )+c_1 e^{-x}+c_2 e^{2 x} \]