Internal problem ID [15313]
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: 543.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime \prime }+y^{\prime \prime }=x^{2}+x} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$4)+diff(y(x),x$2)=x^2+x,y(x), singsol=all)
\[ y \left (x \right ) = \frac {x^{3}}{6}-x^{2}+\frac {x^{4}}{12}-\cos \left (x \right ) c_{1} -\sin \left (x \right ) c_{2} +c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.073 (sec). Leaf size: 43
DSolve[y''''[x]+y''[x]==x^2+x,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^4}{12}+\frac {x^3}{6}-x^2+c_4 x-c_1 \cos (x)-c_2 \sin (x)+c_3 \]