Internal problem ID [2188]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 20, page 90
Problem number: 15.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
\[ \boxed {y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }={\mathrm e}^{2 x}+\sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 34
dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)-4*diff(y(x),x)=exp(2*x)+sin(x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {c_{2} {\mathrm e}^{4 x}}{4}-{\mathrm e}^{-x} c_{1} +\frac {3 \sin \left (x \right )}{34}-\frac {{\mathrm e}^{2 x}}{12}+\frac {5 \cos \left (x \right )}{34}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.267 (sec). Leaf size: 49
DSolve[y'''[x]-3*y''[x]-4*y'[x]==Exp[2*x]+Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\frac {e^{2 x}}{12}+\frac {3 \sin (x)}{34}+\frac {5 \cos (x)}{34}+c_1 \left (-e^{-x}\right )+\frac {1}{4} c_2 e^{4 x}+c_3 \]