8.11.9 problem 9

Internal problem ID [877]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 9
Date solved : Monday, January 27, 2025 at 03:12:32 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }-3 y&=1+x \,{\mathrm e}^{x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 36

dsolve(diff(y(x),x$2)+2*diff(y(x),x)-3*y(x)=1+x*exp(x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.038 (sec). Leaf size: 38

DSolve[D[y[x],{x,2}]+2*D[y[x],x]-3*y[x]==1+x*Exp[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{64} e^x \left (8 x^2-4 x+1+64 c_2\right )+c_1 e^{-3 x}-\frac {1}{3} \]