Internal problem ID [15319]
Book: A book of problems in ordinary differential equations. M.L. KRASNOV, A.L. KISELYOV,
G.I. MARKARENKO. MIR, MOSCOW. 1983
Section: Chapter 2 (Higher order ODE’s). Section 15.3 Nonhomogeneous linear equations with
constant coefficients. Trial and error method. Exercises page 132
Problem number: 549.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-4 y^{\prime }+5 y={\mathrm e}^{2 x} \left (\sin \left (x \right )+2 \cos \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 27
dsolve(diff(y(x),x$2)-4*diff(y(x),x)+5*y(x)=exp(2*x)*(sin(x)+2*cos(x)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\left (x -2 c_{1} -2\right ) \cos \left (x \right )-2 \sin \left (x \right ) \left (c_{2} +x \right )\right ) {\mathrm e}^{2 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.047 (sec). Leaf size: 36
DSolve[y''[x]-4*y'[x]+5*y[x]==Exp[2*x]*(Sin[x]+Cos[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{2} e^{2 x} ((-x+1+2 c_2) \cos (x)+(x+2 c_1) \sin (x)) \]