Internal problem ID [15312]
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: 542.
ODE order: 2.
ODE degree: 1.
CAS Maple gives this as type [[_2nd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime }-2 y^{\prime }+y=x^{3}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 25
dsolve(diff(y(x),x$2)-2*diff(y(x),x)+y(x)=x^3,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{1} x +c_{2} \right ) {\mathrm e}^{x}+x^{3}+6 x^{2}+18 x +24 \]
✓ Solution by Mathematica
Time used: 0.014 (sec). Leaf size: 31
DSolve[y''[x]-2*y'[x]+y[x]==x^3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to x^3+6 x^2+x \left (18+c_2 e^x\right )+c_1 e^x+24 \]