35.6.25 problem 25

Internal problem ID [6175]
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
Date solved : Monday, January 27, 2025 at 01:46:34 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }-3 y&=16 x^{2} {\mathrm e}^{-x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (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)
 

\[ y = \frac {\left (-8 x^{3}-6 x^{2}+6 c_1 -3 x \right ) {\mathrm e}^{-x}}{6}+c_2 \,{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.047 (sec). Leaf size: 37

DSolve[D[y[x],{x,2}]-2*D[y[x],x]-3*y[x]==16*x*Exp[-x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{4} e^{-x} \left (-8 x^2-4 x+4 c_2 e^{4 x}-1+4 c_1\right ) \]