75.16.67 problem 540

Internal problem ID [17040]
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 : 540
Date solved : Tuesday, January 28, 2025 at 09:47:23 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 26

dsolve(diff(y(x),x$3)-diff(y(x),x$2)+diff(y(x),x)-y(x)=x+x^2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.004 (sec). Leaf size: 31

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

\[ y(x)\to -x^2-3 x+c_3 e^x+c_1 \cos (x)+c_2 \sin (x)-1 \]