Internal problem ID [3261]
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]]
\[ \boxed {y^{\prime \prime \prime }-4 y^{\prime \prime }+3 y^{\prime }=x^{2}+x \,{\mathrm e}^{2 x}} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 41
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)
\[ y \left (x \right ) = \frac {\left (1-2 x \right ) {\mathrm e}^{2 x}}{4}+\frac {x^{3}}{9}+\frac {4 x^{2}}{9}+\frac {c_{1} {\mathrm e}^{3 x}}{3}+c_{2} {\mathrm e}^{x}+\frac {26 x}{27}+c_{3} \]
✓ Solution by Mathematica
Time used: 0.239 (sec). Leaf size: 58
DSolve[y'''[x]-4*y''[x]+3*y'[x]==x^2+x*Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to \frac {x^3}{9}+\frac {4 x^2}{9}+\frac {26 x}{27}+\frac {1}{4} e^{2 x} (1-2 x)+c_1 e^x+\frac {1}{3} c_2 e^{3 x}+c_3 \]