Internal problem ID [2242]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 24, page 109
Problem number: 10.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+2 y^{\prime \prime }=x \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 42
dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)=x*cos(2*x),y(x), singsol=all)
\[ y = -\frac {\cos \left (2 x \right )}{16}-\frac {\sin \left (2 x \right ) x}{16}+\frac {c_{1} {\mathrm e}^{-2 x}}{4}+\frac {3 \sin \left (2 x \right )}{32}-\frac {\cos \left (2 x \right ) x}{16}+c_{2} x +c_{3} \]
✓ Solution by Mathematica
Time used: 1.447 (sec). Leaf size: 48
DSolve[y'''[x]+2*y''[x]==x*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 x+\frac {1}{16} \left (-x \sin (2 x)-(x+1) \cos (2 x)+4 c_1 e^{-2 x}+3 \sin (x) \cos (x)\right )+c_2 \]