Internal problem ID [15356]
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: 587.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime }=x \,{\mathrm e}^{2 x}+\sin \left (x \right )+x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 44
dsolve(diff(y(x),x$3)-4*diff(y(x),x)=x*exp(2*x)+sin(x)+x^2,y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (8 x^{2}+64 c_{1} -12 x +7\right ) {\mathrm e}^{2 x}}{128}-\frac {x^{3}}{12}-\frac {c_{2} {\mathrm e}^{-2 x}}{2}-\frac {x}{8}+c_{3} +\frac {\cos \left (x \right )}{5} \]
✓ Solution by Mathematica
Time used: 0.617 (sec). Leaf size: 60
DSolve[y'''[x]-4*y'[x]==x*Exp[2*x]+Sin[x]+x^2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {x^3}{12}+\frac {1}{128} e^{2 x} \left (8 x^2-12 x+7+64 c_1\right )-\frac {x}{8}+\frac {\cos (x)}{5}-\frac {1}{2} c_2 e^{-2 x}+c_3 \]