Internal problem ID [2231]
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: 32.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+y^{\prime \prime }-2 y^{\prime }={\mathrm e}^{-2 x} \cos \left (2 x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 38
dsolve(diff(y(x),x$3)+diff(y(x),x$2)-2*diff(y(x),x)=exp(-2*x)*cos(2*x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {{\mathrm e}^{-2 x} \left (-2 c_{2} {\mathrm e}^{3 x}-2 c_{3} {\mathrm e}^{2 x}+c_{1} -\frac {5 \cos \left (2 x \right )}{52}-\frac {\sin \left (2 x \right )}{52}\right )}{2} \]
✓ Solution by Mathematica
Time used: 0.872 (sec). Leaf size: 42
DSolve[y'''[x]+y''[x]-2*y'[x]==Exp[-2*x]*Cos[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{104} e^{-2 x} \left (\sin (2 x)+5 \cos (2 x)-52 \left (c_1-2 c_2 e^{3 x}\right )\right )+c_3 \]