75.16.44 problem 517

Internal problem ID [17017]
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 ODEs). Section 15.3 Nonhomogeneous linear equations with constant coefficients. Trial and error method. Exercises page 132
Problem number : 517
Date solved : Tuesday, January 28, 2025 at 09:45:37 AM
CAS classification : [[_high_order, _missing_x]]

\begin{align*} y^{\prime \prime \prime \prime }-2 y^{\prime \prime \prime }+2 y^{\prime \prime }-2 y^{\prime }+y&=1 \end{align*}

✓ Solution by Maple

Time used: 0.006 (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)
 

\[ y = \left (c_4 x +c_{2} \right ) {\mathrm e}^{x}+\cos \left (x \right ) c_{1} +c_{3} \sin \left (x \right )+1 \]

✓ Solution by Mathematica

Time used: 0.003 (sec). Leaf size: 30

DSolve[D[y[x],{x,4}]-2*D[y[x],{x,3}]+2*D[y[x],{x,2}]-2*D[y[x],x]+y[x]==1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to c_3 e^x+c_4 e^x x+c_1 \cos (x)+c_2 \sin (x)+1 \]