Internal problem ID [2751]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 19.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _linear, _nonhomogeneous]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-2 y^{\prime \prime }+4 y^{\prime }-8 y-{\mathrm e}^{2 x} \sin \left (2 x \right )-2 x^{2}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 96
dsolve(diff(y(x),x$3)-2*diff(y(x),x$2)+4*diff(y(x),x)-8*y(x)=exp(2*x)*sin(2*x)+2*x^2,y(x), singsol=all)
\[ y \relax (x ) = -\frac {{\mathrm e}^{-2 x} \left (5 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{4 x}\right ) \cos \left (2 x \right )}{80}+\frac {{\mathrm e}^{-2 x} \left (5 \,{\mathrm e}^{2 x}-4 \,{\mathrm e}^{4 x}\right ) \sin \left (2 x \right )}{80}-\frac {{\mathrm e}^{-2 x} \left (4 \,{\mathrm e}^{2 x} x^{2}+4 \,{\mathrm e}^{2 x} x +{\mathrm e}^{4 x}\right )}{16}+\cos \left (2 x \right ) c_{1}+c_{2} {\mathrm e}^{2 x}+c_{3} \sin \left (2 x \right ) \]
✓ Solution by Mathematica
Time used: 0.219 (sec). Leaf size: 58
DSolve[y'''[x]-2*y''[x]+4*y'[x]-8*y[x]==Exp[2*x]*Sin[2*x]+2*x^2,y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{80} \left (-20 \left (x^2+x-4 c_1 \cos (2 x)-4 c_2 \sin (2 x)\right )-e^{2 x} (4 \sin (2 x)+2 \cos (2 x)+5-80 c_3)\right ) \\ \end{align*}