Internal problem ID [15355]
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: 586.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-y^{\prime \prime }-2 y^{\prime }=4 x +3 \sin \left (x \right )+\cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$3)-diff(y(x),x$2)-2*diff(y(x),x)=4*x+3*sin(x)+cos(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{1} {\mathrm e}^{2 x}}{2}-c_{2} {\mathrm e}^{-x}-x^{2}+\cos \left (x \right )+x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.338 (sec). Leaf size: 46
DSolve[y'''[x]-y''[x]-2*y'[x]==4*x+2*Sin[x]+Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -x^2+x-\frac {\sin (x)}{10}+\frac {7 \cos (x)}{10}-c_1 e^{-x}+\frac {1}{2} c_2 e^{2 x}+c_3 \]