75.16.22 problem 495

Internal problem ID [16995]
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 : 495
Date solved : Tuesday, January 28, 2025 at 09:45:20 AM
CAS classification : [[_high_order, _missing_x]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 55

dsolve(diff(y(x),x$4)-diff(y(x),x)=2,y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.603 (sec). Leaf size: 70

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

\[ y(x)\to \int _1^x\left (e^{K[1]} c_1+e^{-\frac {K[1]}{2}} c_2 \cos \left (\frac {1}{2} \sqrt {3} K[1]\right )+e^{-\frac {K[1]}{2}} c_3 \sin \left (\frac {1}{2} \sqrt {3} K[1]\right )-2\right )dK[1]+c_4 \]