Internal problem ID [2233]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 23, page 106
Problem number: 34.
ODE order: 4.
ODE degree: 1.
CAS Maple gives this as type [[_high_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime \prime }-y=\cos \left (x \right ) x^{2}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 45
dsolve(diff(y(x),x$4)-y(x)=x^2*cos(x),y(x), singsol=all)
\[ y = \left (-\frac {3 x^{2}}{8}+\frac {1}{4}\right ) \cos \left (x \right )+\left (\frac {5}{8} x -\frac {1}{12} x^{3}\right ) \sin \left (x \right )+\cos \left (x \right ) c_{1} +c_{2} {\mathrm e}^{x}+c_{3} \sin \left (x \right )+c_{4} {\mathrm e}^{-x} \]
✓ Solution by Mathematica
Time used: 0.092 (sec). Leaf size: 54
DSolve[y''''[x]-y[x]==x^2*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \left (-\frac {x^3}{12}+\frac {5 x}{8}+c_4\right ) \sin (x)+\left (-\frac {3 x^2}{8}+\frac {5}{16}+c_2\right ) \cos (x)+c_1 e^x+c_3 e^{-x} \]