Internal problem ID [15266]
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: 496.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-y^{\prime \prime }=3} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 24
dsolve(diff(y(x),x$4)-diff(y(x),x$2)=3,y(x), singsol=all)
\[ y \left (x \right ) = c_{2} {\mathrm e}^{x}-\frac {3 x^{2}}{2}+c_{1} {\mathrm e}^{-x}+c_{3} x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.045 (sec). Leaf size: 33
DSolve[y''''[x]-y''[x]==3,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {3 x^2}{2}+c_4 x+c_1 e^x+c_2 e^{-x}+c_3 \]