Internal problem ID [15287]
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: 517.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y=1} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 22
dsolve(diff(y(x),x$4)-2*diff(y(x),x$3)+2*diff(y(x),x$2)-2*diff(y(x),x)+y(x)=1,y(x), singsol=all)
\[ y \left (x \right ) = \left (c_{4} x +c_{2} \right ) {\mathrm e}^{x}+\cos \left (x \right ) c_{1} +c_{3} \sin \left (x \right )+1 \]
✓ Solution by Mathematica
Time used: 0.003 (sec). Leaf size: 30
DSolve[y''''[x]-2*y'''[x]+2*y''[x]-2*y'[x]+y[x]==1,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 e^x+c_4 e^x x+c_1 \cos (x)+c_2 \sin (x)+1 \]