Internal problem ID [15304]
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: 534.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }+2 y^{\prime }=4 \,{\mathrm e}^{x} \left (\sin \left (x \right )+\cos \left (x \right )\right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 32
dsolve(diff(y(x),x$2)+2*diff(y(x),x)=4*exp(x)*(sin(x)+cos(x)),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {\left (\frac {4 \left (\cos \left (x \right )-3 \sin \left (x \right )\right ) {\mathrm e}^{3 x}}{5}-2 c_{2} {\mathrm e}^{2 x}+c_{1} \right ) {\mathrm e}^{-2 x}}{2} \]
✓ Solution by Mathematica
Time used: 0.229 (sec). Leaf size: 37
DSolve[y''[x]+2*y'[x]==4*Exp[x]*(Sin[x]+Cos[x]),y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {6}{5} e^x \sin (x)-\frac {2}{5} e^x \cos (x)-\frac {1}{2} c_1 e^{-2 x}+c_2 \]