Internal problem ID [5386]
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: 16.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-y={\mathrm e}^{x} \sin \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 30
dsolve(diff(y(x),x$2)-y(x)=exp(x)*sin(2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{x} \cos \left (2 x \right )}{8}+c_{2} {\mathrm e}^{-x}+{\mathrm e}^{x} \left (c_{1} -\frac {\sin \left (2 x \right )}{8}\right ) \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 37
DSolve[y''[x]-y[x]==Exp[x]*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_1 e^x+c_2 e^{-x}-\frac {1}{8} e^x (\sin (2 x)+\cos (2 x)+2) \]