Internal problem ID [5402]
Book: Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres.
McGraw Hill 1952
Section: Chapter 16. Linear equations with constant coefficients (Short methods). Supplemetary
problems. Page 107
Problem number: 37.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }-y=\cos \left (x \right ) {\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)-2*diff(y(x),x)-y(x)=exp(x)*cos(x),y(x), singsol=all)
\[ y = {\mathrm e}^{x \left (1+\sqrt {2}\right )} c_{2} +c_{1} {\mathrm e}^{-x \left (\sqrt {2}-1\right )}-\frac {\cos \left (x \right ) {\mathrm e}^{x}}{3} \]
✓ Solution by Mathematica
Time used: 0.159 (sec). Leaf size: 56
DSolve[y''[x]-2*y'[x]-y[x]==Exp[x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{3} e^{-\sqrt {2} x} \left (-e^{\left (1+\sqrt {2}\right ) x} \cos (x)+3 e^x \left (c_2 e^{2 \sqrt {2} x}+c_1\right )\right ) \]