7.11.13 problem 13

Internal problem ID [334]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 13
Date solved : Wednesday, February 05, 2025 at 03:21:03 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+2 y^{\prime }+5 y&={\mathrm e}^{x} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

dsolve(diff(y(x),x$2)+2*diff(y(x),x)+5*y(x)=exp(x)*sin(x),y(x), singsol=all)
 

\[ y = \left (\sin \left (2 x \right ) c_2 +\cos \left (2 x \right ) c_1 \right ) {\mathrm e}^{-x}-\frac {4 \left (\cos \left (x \right )-\frac {7 \sin \left (x \right )}{4}\right ) {\mathrm e}^{x}}{65} \]

✓ Solution by Mathematica

Time used: 0.216 (sec). Leaf size: 48

DSolve[D[y[x],{x,2}]+2*D[y[x],x]+5*y[x]==Exp[x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {7}{65} e^x \sin (x)-\frac {4}{65} e^x \cos (x)+c_2 e^{-x} \cos (2 x)+c_1 e^{-x} \sin (2 x) \]