Internal problem ID [5392]
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: 26.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }+y^{\prime }+y={\mathrm e}^{3 x}+6 \,{\mathrm e}^{x}-3 \,{\mathrm e}^{-2 x}+5} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve(diff(y(x),x$2)+diff(y(x),x)+y(x)=exp(3*x)+6*exp(x)-3*exp(-2*x)+5,y(x), singsol=all)
\[ y \left (x \right ) = \left (\frac {{\mathrm e}^{5 x}}{13}+2 \,{\mathrm e}^{3 x}+\sin \left (\frac {\sqrt {3}\, x}{2}\right ) c_{2} {\mathrm e}^{\frac {3 x}{2}}+\cos \left (\frac {\sqrt {3}\, x}{2}\right ) c_{1} {\mathrm e}^{\frac {3 x}{2}}+5 \,{\mathrm e}^{2 x}-1\right ) {\mathrm e}^{-2 x} \]
✓ Solution by Mathematica
Time used: 6.996 (sec). Leaf size: 70
DSolve[y''[x]+y'[x]+y[x]==Exp[3*x]+6*Exp[x]-3*Exp[-2*x]+5,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -e^{-2 x}+2 e^x+\frac {e^{3 x}}{13}+c_2 e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+c_1 e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+5 \]