Internal problem ID [4323]
Book: Mathematical Methods in the Physical Sciences. third edition. Mary L. Boas. John Wiley.
2006
Section: Chapter 8, Ordinary differential equations. Section 6. SECOND-ORDER LINEAR
EQUATIONSWITH CONSTANT COEFFICIENTS AND RIGHT-HAND SIDE NOT ZERO. page
422
Problem number: 25.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-2 y^{\prime }-3 y-16 x^{2} {\mathrm e}^{-x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-3*y(x)=16*x^2*exp(-x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{3 x}-\frac {x \left (8 x^{2}+6 x +3\right ) {\mathrm e}^{-x}}{6} \]
✓ Solution by Mathematica
Time used: 0.027 (sec). Leaf size: 37
DSolve[y''[x]-2*y'[x]-3*y[x]==16*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{-x} \left (-4 x (2 x+1)+4 c_2 e^{4 x}-1+4 c_1\right ) \\ \end{align*}