8.11.26 problem 49

Internal problem ID [894]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 49
Date solved : Monday, January 27, 2025 at 03:16:46 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 17

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+4*y(x)=2*exp(2*x),y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 21

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

\[ y(x)\to e^{2 x} \left (x^2+c_2 x+c_1\right ) \]