Internal problem ID [5388]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 15. Linear equations with constant coefficients (Variation of parameters).
Supplemetary problems. Page 98
Problem number: 18.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-9 y=x +{\mathrm e}^{2 x}-\sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 40
dsolve(diff(y(x),x$2)-9*y(x)=x+exp(2*x)-sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-3 x} \left (\left (x -\frac {9 \sin \left (2 x \right )}{13}\right ) {\mathrm e}^{3 x}-9 \,{\mathrm e}^{6 x} c_{1} -9 c_{2} +\frac {9 \,{\mathrm e}^{5 x}}{5}\right )}{9} \]
✓ Solution by Mathematica
Time used: 0.846 (sec). Leaf size: 44
DSolve[y''[x]-9*y[x]==x+Exp[2*x]-Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x}{9}-\frac {e^{2 x}}{5}+\frac {1}{13} \sin (2 x)+c_1 e^{3 x}+c_2 e^{-3 x} \]