20.7.14 problem Problem 39

Internal problem ID [3729]
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 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 39
Date solved : Monday, January 27, 2025 at 07:56:29 AM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+6 y&=7 \,{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 27

dsolve(diff(y(x),x$2)-4*diff(y(x),x)+6*y(x)=7*exp(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = {\mathrm e}^{2 x} \left (\frac {7}{2}+c_{2} \sin \left (\sqrt {2}\, x \right )+\cos \left (\sqrt {2}\, x \right ) c_{1} \right ) \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 40

DSolve[D[y[x],{x,2}]-4*D[y[x],x]+6*y[x]==7*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{2} e^{2 x} \left (2 c_2 \cos \left (\sqrt {2} x\right )+2 c_1 \sin \left (\sqrt {2} x\right )+7\right ) \]