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]]
\[ \boxed {y^{\prime \prime \prime \prime }-y=x^{2} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.015 (sec). Leaf size: 45
dsolve(diff(y(x),x$4)-y(x)=x^2*cos(x),y(x), singsol=all)
\[ y \left (x \right ) = c_{4} {\mathrm e}^{-x}+\frac {\left (-3 x^{2}+8 c_{1} +2\right ) \cos \left (x \right )}{8}+\frac {\left (-2 x^{3}+24 c_{3} +15 x \right ) \sin \left (x \right )}{24}+c_{2} {\mathrm e}^{x} \]
✓ 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]
\[ y(x)\to \left (-\frac {x^3}{12}+\frac {5 x}{8}+c_4\right ) \sin (x)+\left (-\frac {3 x^2}{8}+\frac {5}{16}+c_2\right ) \cos (x)+c_1 e^x+c_3 e^{-x} \]