8.11.15 problem 26

Internal problem ID [883]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 26
Date solved : Wednesday, February 05, 2025 at 04:36:51 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-6 y^{\prime }+13 y&=x \,{\mathrm e}^{3 x} \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 34

dsolve(diff(y(x),x$2)-6*diff(y(x),x)+13*y(x)=x*exp(3*x)*sin(2*x),y(x), singsol=all)
 

\[ y = -\frac {\left (\left (x^{2}-8 c_1 \right ) \cos \left (2 x \right )-\frac {\sin \left (2 x \right ) \left (x +16 c_2 \right )}{2}\right ) {\mathrm e}^{3 x}}{8} \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 43

DSolve[D[y[x],{x,2}]-6*D[y[x],x]+13*y[x]==x*Exp[3*x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{64} e^{3 x} \left (\left (-8 x^2+1+64 c_2\right ) \cos (2 x)+4 (x+16 c_1) \sin (2 x)\right ) \]