78.16.27 problem 25 (c)

Internal problem ID [18406]
Book : DIFFERENTIAL EQUATIONS WITH APPLICATIONS AND HISTORICAL NOTES by George F. Simmons. 3rd edition. 2017. CRC press, Boca Raton FL.
Section : Chapter 3. Second order linear equations. Section 23. Operator Methods for Finding Particular Solutions. Problems at page 169
Problem number : 25 (c)
Date solved : Tuesday, January 28, 2025 at 11:49:31 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-4 y^{\prime }+4 y&={\mathrm e}^{2 x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 18

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

\[ y = {\mathrm e}^{2 x} \left (c_{2} +c_{1} x -\sin \left (x \right )\right ) \]

✓ Solution by Mathematica

Time used: 0.028 (sec). Leaf size: 22

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

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