75.16.70 problem 543

Internal problem ID [17043]
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 : 543
Date solved : Tuesday, January 28, 2025 at 09:47:25 AM
CAS classification : [[_high_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 34

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

\[ y = \frac {x^{3}}{6}-x^{2}+\frac {x^{4}}{12}-\cos \left (x \right ) c_{1} -\sin \left (x \right ) c_{2} +c_{3} x +c_4 \]

✓ Solution by Mathematica

Time used: 60.021 (sec). Leaf size: 47

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

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