Internal problem ID [221]
Book: Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section: Section 5.5, Nonhomogeneous equations and undetermined coefficients Page
351
Problem number: 3.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y^{\prime }-6 y=2 \sin \left (3 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$2)-diff(y(x),x)-6*y(x)=2*sin(3*x),y(x), singsol=all)
\[ y \left (x \right ) = {\mathrm e}^{-2 x} \left (\frac {\left (\cos \left (3 x \right )-5 \sin \left (3 x \right )\right ) {\mathrm e}^{2 x}}{39}+c_{2} {\mathrm e}^{5 x}+c_{1} \right ) \]
✓ Solution by Mathematica
Time used: 0.021 (sec). Leaf size: 37
DSolve[y''[x]-y'[x]-6*y[x]==2*Sin[3*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^{-2 x}+c_2 e^{3 x}+\frac {1}{39} (\cos (3 x)-5 \sin (3 x)) \]