Internal problem ID [15265]
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: 495.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _missing_x]]
\[ \boxed {y^{\prime \prime \prime \prime }-y^{\prime }=2} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 55
dsolve(diff(y(x),x$4)-diff(y(x),x)=2,y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-\frac {x}{2}} \left (\sqrt {3}\, c_{3} +c_{2} \right ) \cos \left (\frac {x \sqrt {3}}{2}\right )}{2}+\frac {{\mathrm e}^{-\frac {x}{2}} \left (\sqrt {3}\, c_{2} -c_{3} \right ) \sin \left (\frac {x \sqrt {3}}{2}\right )}{2}+c_{1} {\mathrm e}^{x}-2 x +c_{4} \]
✓ Solution by Mathematica
Time used: 0.219 (sec). Leaf size: 85
DSolve[y''''[x]-y'[x]==2,y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -2 x+c_1 e^x-\frac {1}{2} \left (c_2+\sqrt {3} c_3\right ) e^{-x/2} \cos \left (\frac {\sqrt {3} x}{2}\right )+\frac {1}{2} \left (\sqrt {3} c_2-c_3\right ) e^{-x/2} \sin \left (\frac {\sqrt {3} x}{2}\right )+c_4 \]