28.2.51 problem 51

Internal problem ID [4494]
Book : Differential equations for engineers by Wei-Chau XIE, Cambridge Press 2010
Section : Chapter 4. Linear Differential Equations. Page 183
Problem number : 51
Date solved : Monday, January 27, 2025 at 09:21:40 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y&=12 \,{\mathrm e}^{2 x}+4 \,{\mathrm e}^{3 x} \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 38

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+4*y(x)=12*exp(2*x)+4*exp(3*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \frac {\left (18 x^{2}+\left (9 c_3 -12\right ) x +9 c_{2} +4\right ) {\mathrm e}^{2 x}}{9}+{\mathrm e}^{-x} c_{1} +{\mathrm e}^{3 x} \]

✓ Solution by Mathematica

Time used: 0.094 (sec). Leaf size: 44

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+4*y[x]==12*Exp[2*x]+4*Exp[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (2 x^2+\left (-\frac {4}{3}+c_3\right ) x+\frac {4}{9}+c_2\right )+e^{3 x}+c_1 e^{-x} \]