20.9.27 problem Problem 27

Internal problem ID [3771]
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
Date solved : Monday, January 27, 2025 at 08:01:09 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&=5 x \,{\mathrm e}^{2 x} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=1\\ y^{\prime }\left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.018 (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)
 

\[ y \left (x \right ) = \frac {{\mathrm e}^{2 x} \left (5 x^{3}-12 x +6\right )}{6} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 24

DSolve[{D[y[x],{x,2}]-4*D[y[x],x]+4*y[x]==5*x*Exp[2*x],{y[0]==1,Derivative[1][y][0] ==0}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{6} e^{2 x} \left (5 x^3-12 x+6\right ) \]