Internal problem ID [2237]
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: 4.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }+4 y^{\prime }={\mathrm e}^{x}+\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 28
dsolve(diff(y(x),x$3)+4*diff(y(x),x)=exp(x)+sin(x),y(x), singsol=all)
\[ y = \frac {\sin \left (2 x \right ) c_{1}}{2}-\frac {c_{2} \cos \left (2 x \right )}{2}+\frac {{\mathrm e}^{x}}{5}-\frac {\cos \left (x \right )}{3}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.241 (sec). Leaf size: 37
DSolve[y'''[x]+4*y'[x]==Exp[x]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {e^x}{5}-\frac {1}{2} c_2 \cos (2 x)+\cos (x) \left (-\frac {1}{3}+c_1 \sin (x)\right )+c_3 \]