Internal problem ID [2211]
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: 10.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+y^{\prime }-4 y=\sin \left (x \right )-{\mathrm e}^{4 x}} \]
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 41
dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+diff(y(x),x)-4*y(x)=sin(x)-exp(4*x),y(x), singsol=all)
\[ y \left (x \right ) = \frac {\left (8-17 x +289 c_{3} \right ) {\mathrm e}^{4 x}}{289}+\frac {\left (68 x +578 c_{1} +15\right ) \cos \left (x \right )}{578}-\frac {\sin \left (x \right ) \left (x -34 c_{2} +\frac {8}{17}\right )}{34} \]
✓ Solution by Mathematica
Time used: 0.149 (sec). Leaf size: 52
DSolve[y'''[x]-4*y''[x]+y'[x]-4*y[x]==Sin[x]-Exp[4*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {1}{289} e^{4 x} (-17 x+8+289 c_3)+\left (\frac {2 x}{17}+\frac {13}{1156}+c_1\right ) \cos (x)+\left (-\frac {x}{34}-\frac {21}{289}+c_2\right ) \sin (x) \]