7.11.11 problem 11

Internal problem ID [332]
Book : Elementary Differential Equations. By C. Henry Edwards, David E. Penney and David Calvis. 6th edition. 2008
Section : Chapter 2. Linear Equations of Higher Order. Section 2.5 (Nonhomogeneous equations and undetermined coefficients). Problems at page 161
Problem number : 11
Date solved : Wednesday, February 05, 2025 at 03:21:02 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&=3 x -1 \end{align*}

✓ Solution by Maple

Time used: 0.001 (sec). Leaf size: 28

dsolve(diff(y(x),x$3)+4*diff(y(x),x)=3*x-1,y(x), singsol=all)
 

\[ y = \frac {3 x^{2}}{8}+\frac {c_1 \sin \left (2 x \right )}{2}-\frac {c_2 \cos \left (2 x \right )}{2}-\frac {x}{4}+c_3 \]

✓ Solution by Mathematica

Time used: 0.103 (sec). Leaf size: 38

DSolve[D[y[x],{x,3}]+4*D[y[x],x]==3*x-1,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{8} \left (3 x^2-2 x-4 c_2 \cos (2 x)+4 c_1 \sin (2 x)+8 c_3\right ) \]