Internal problem ID [15353]
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: 584.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+y^{\prime }=2 x +{\mathrm e}^{x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)+diff(y(x),x)=2*x+exp(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (x^{2}+\left (2 c_{1} -2\right ) x -2 c_{1} +2 c_{2} +2\right ) {\mathrm e}^{x}}{2}+x^{2}+4 x +c_{3} \]
✓ Solution by Mathematica
Time used: 0.268 (sec). Leaf size: 39
DSolve[y'''[x]-2*y''[x]+y'[x]==2*x+Exp[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^2+e^x \left (\frac {x^2}{2}+(-1+c_2) x+1+c_1-c_2\right )+4 x+c_3 \]