Internal problem ID [2156]
Book: Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath.
Boston. 1964
Section: Exercise 19, page 86
Problem number: 17.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y={\mathrm e}^{4 x} \sin \left (x \right )} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 35
dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+diff(y(x),x)-4*y(x)=exp(4*x)*sin(x),y(x), singsol=all)
\[ y = -\frac {\cos \left (x \right ) {\mathrm e}^{4 x}}{20}-\frac {{\mathrm e}^{4 x} \sin \left (x \right )}{40}+\cos \left (x \right ) c_{1} +\sin \left (x \right ) c_{2} +c_{3} {\mathrm e}^{4 x} \]
✓ Solution by Mathematica
Time used: 0.098 (sec). Leaf size: 44
DSolve[y'''[x]-4*y''[x]+y'[x]-4*y[x]==Exp[4*x]*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to c_3 e^{4 x}+\left (-\frac {e^{4 x}}{20}+c_1\right ) \cos (x)+\left (-\frac {e^{4 x}}{40}+c_2\right ) \sin (x) \]