Internal problem ID [4329]
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: 38.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-9 \,{\mathrm e}^{-x} x +6 x^{2}-4 \,{\mathrm e}^{2 x}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 50
dsolve(diff(y(x),x$2)-2*diff(y(x),x)=9*x*exp(-x)-6*x^2+4*exp(2*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{2 x}}{2}+\frac {3 x^{2}}{2}+x^{3}+2 \,{\mathrm e}^{2 x} x -{\mathrm e}^{2 x}+3 x \,{\mathrm e}^{-x}+4 \,{\mathrm e}^{-x}+\frac {3 x}{2}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.493 (sec). Leaf size: 48
DSolve[y''[x]-2*y'[x]==9*x*Exp[-x]-6*x^2+4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{2} \left (e^{-x} (6 x+8)+x (x (2 x+3)+3)+e^{2 x} (4 x-2+c_1)\right )+c_2 \\ \end{align*}