Internal problem ID [2150]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 11.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-6 y=x^{3}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 39
dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=x^3,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} \left (\left (x^{3}-\frac {1}{2} x^{2}+\frac {7}{6} x -\frac {13}{36}\right ) {\mathrm e}^{2 x}-6 c_{2} {\mathrm e}^{5 x}-6 c_{1} \right )}{6} \]
✓ Solution by Mathematica
Time used: 0.022 (sec). Leaf size: 41
DSolve[y''[x]-y'[x]-6*y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{216} \left (-36 x^3+18 x^2-42 x+13\right )+c_1 e^{-2 x}+c_2 e^{3 x} \]