Internal problem ID [2291]
Book: Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition,
2015
Section: Chapter 8, Linear differential equations of order n. Section 8.7, The Variation of Parameters
Method. page 556
Problem number: Problem 27.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime }-4 y^{\prime }+4 y-5 x \,{\mathrm e}^{2 x}=0} \end {gather*} With initial conditions \begin {align*} [y \relax (0) = 1, y^{\prime }\relax (0) = 0] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 20
dsolve([diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=5*x*exp(2*x),y(0) = 1, D(y)(0) = 0],y(x), singsol=all)
\[ y \relax (x ) = \frac {{\mathrm e}^{2 x} \left (5 x^{3}-12 x +6\right )}{6} \]
✓ Solution by Mathematica
Time used: 0.006 (sec). Leaf size: 24
DSolve[{y''[x]-4*y'[x]+4*y[x]==5*x*Exp[2*x],{y[0]==1,y'[0]==0}},y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{6} e^{2 x} \left (5 x^3-12 x+6\right ) \\ \end{align*}