Internal problem ID [15346]
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. Superposition principle. Exercises page 137
Problem number: 577.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _missing_y]]
\[ \boxed {y^{\prime \prime }-3 y^{\prime }=1+{\mathrm e}^{x}+\cos \left (x \right )+\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$2)-3*diff(y(x),x)=1+exp(x)+cos(x)+sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{3 x}}{3}-\frac {2 \sin \left (x \right )}{5}-\frac {{\mathrm e}^{x}}{2}+\frac {\cos \left (x \right )}{5}-\frac {x}{3}+c_{2} \]
✓ Solution by Mathematica
Time used: 0.261 (sec). Leaf size: 43
DSolve[y''[x]-3*y'[x]==1+Exp[x]+Cos[x]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x}{3}-\frac {e^x}{2}-\frac {2 \sin (x)}{5}+\frac {\cos (x)}{5}+\frac {1}{3} c_1 e^{3 x}+c_2 \]