Internal problem ID [2230]
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: 31.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime \prime }+5 y^{\prime }={\mathrm e}^{-2 x} \cos \left (x \right )} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 70
dsolve(diff(y(x),x$3)+4*diff(y(x),x$2)+5*diff(y(x),x)=exp(-2*x)*cos(x),y(x), singsol=all)
\[ y = c_{2} \left (-\frac {{\mathrm e}^{-2 x} \cos \left (x \right )}{5}-\frac {2 \,{\mathrm e}^{-2 x} \sin \left (x \right )}{5}\right )+\frac {\left (-\frac {x}{5}-\frac {4}{25}\right ) {\mathrm e}^{-2 x} \cos \left (x \right )}{2}+\frac {\left (-\frac {2 x}{5}-\frac {3}{25}\right ) {\mathrm e}^{-2 x} \sin \left (x \right )}{2}+c_{1} \left (-\frac {2 \,{\mathrm e}^{-2 x} \cos \left (x \right )}{5}+\frac {{\mathrm e}^{-2 x} \sin \left (x \right )}{5}\right )+c_{3} \]
✓ Solution by Mathematica
Time used: 0.337 (sec). Leaf size: 52
DSolve[y'''[x]+4*y''[x]+5*y'[x]==Exp[-2*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{50} e^{-2 x} (2 (-5 x+1-10 c_1+5 c_2) \sin (x)-(5 x+14+10 c_1+20 c_2) \cos (x))+c_3 \]