Internal problem ID [2752]
Book: Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section: Chapter 4. Linear Differential Equations. Page 183
Problem number: 20.
ODE order: 3.
ODE degree: 1.
CAS Maple gives this as type [[_3rd_order, _missing_y]]
Solve \begin {gather*} \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime }-x^{2}-x \,{\mathrm e}^{2 x}=0} \end {gather*}
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 43
dsolve(diff(y(x),x$3)-4*diff(y(x),x$2)+3*diff(y(x),x)=x^2+x*exp(2*x),y(x), singsol=all)
\[ y \relax (x ) = c_{1} {\mathrm e}^{x}+\frac {{\mathrm e}^{3 x} c_{2}}{3}+\frac {4 x^{2}}{9}+\frac {x^{3}}{9}-\frac {{\mathrm e}^{2 x} x}{2}+\frac {{\mathrm e}^{2 x}}{4}+\frac {26 x}{27}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.112 (sec). Leaf size: 52
DSolve[y'''[x]-4*y''[x]+3*y'[x]==x^2+x*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to \frac {1}{4} e^{2 x} (1-2 x)+\frac {1}{27} x (3 x (x+4)+26)+c_1 e^x+\frac {1}{3} c_2 e^{3 x}+c_3 \\ \end{align*}