Internal problem ID [1159]
Book: Elementary differential equations with boundary value problems. William F. Trench.
Brooks/Cole 2001
Section: Chapter 5 linear second order equations. Section 5.7 Variation of Parameters. Page
262
Problem number: 5.
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 }+y-14 x^{\frac {3}{2}} {\mathrm e}^{x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.013 (sec). Leaf size: 21
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=14*x^(3/2)*exp(x),y(x), singsol=all)
\[ y \relax (x ) = c_{2} {\mathrm e}^{x}+x \,{\mathrm e}^{x} c_{1}+\frac {8 x^{\frac {7}{2}} {\mathrm e}^{x}}{5} \]
✓ Solution by Mathematica
Time used: 0.007 (sec). Leaf size: 29
DSolve[y''[x]-2*y'[x]+y[x]==14*x^(3/2)*Exp[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{5} e^x \left (8 x^{7/2}+5 c_2 x+5 c_1\right ) \\ \end{align*}