12.19.9 problem section 9.3, problem 9

Internal problem ID [2156]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 9
Date solved : Monday, January 27, 2025 at 05:42:54 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} 2 y^{\prime \prime \prime }-7 y^{\prime \prime }+4 y^{\prime }+4 y&={\mathrm e}^{2 x} \left (17+30 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.008 (sec). Leaf size: 29

dsolve(2*diff(y(x),x$3)-7*diff(y(x),x$2)+4*diff(y(x),x)+4*y(x)=exp(2*x)*(17+30*x),y(x), singsol=all)
 

\[ y = c_2 \,{\mathrm e}^{-\frac {x}{2}}+\left (x^{3}+\frac {1}{2} x^{2}+c_1 +x c_3 \right ) {\mathrm e}^{2 x} \]

✓ Solution by Mathematica

Time used: 0.032 (sec). Leaf size: 46

DSolve[2*D[y[x],{x,3}]-7*D[y[x],{x,2}]+4*D[y[x],x]+4*y[x]==Exp[2*x]*(17+30*x),y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{2 x} \left (x^3+\frac {x^2}{2}+\left (-\frac {2}{5}+c_3\right ) x+\frac {4}{25}+c_2\right )+c_1 e^{-x/2} \]