Internal problem ID [13511]
Book: Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell.
second edition. CRC Press. FL, USA. 2020
Section: Chapter 25. Review exercises for part III. page 447
Problem number: 33.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-9 y^{\prime }+14 y=576 x^{2} {\mathrm e}^{-x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 33
dsolve(diff(y(x),x$2)-9*diff(y(x),x)+14*y(x)=576*x^2*exp(-x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{7 x} c_{2} +{\mathrm e}^{2 x} c_{1} +\frac {\left (288 x^{2}+264 x +97\right ) {\mathrm e}^{-x}}{12} \]
✓ Solution by Mathematica
Time used: 0.024 (sec). Leaf size: 39
DSolve[y''[x]-9*y'[x]+14*y[x]==576*x^2*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to e^{-x} \left (24 x^2+22 x+c_1 e^{3 x}+c_2 e^{8 x}+\frac {97}{12}\right ) \]