35.6.32 problem 38

Internal problem ID [6182]
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
Date solved : Monday, January 27, 2025 at 01:46:57 PM
CAS classification : [[_2nd_order, _missing_y]]

\begin{align*} y^{\prime \prime }-2 y^{\prime }&=9 x \,{\mathrm e}^{-x}-6 x^{2}+4 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.000 (sec). Leaf size: 39

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)
 

\[ y = \frac {\left (4 x +c_1 -2\right ) {\mathrm e}^{2 x}}{2}+\left (4+3 x \right ) {\mathrm e}^{-x}+x^{3}+\frac {3 x^{2}}{2}+\frac {3 x}{2}+c_2 \]

✓ Solution by Mathematica

Time used: 0.445 (sec). Leaf size: 49

DSolve[D[y[x],{x,2}]-2*D[y[x],x]==9*x*Exp[-x]-6*x^2+4*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} \left (x \left (2 x^2+3 x+3\right )+e^{-x} (6 x+8)+e^{2 x} (4 x-2+c_1)\right )+c_2 \]