15.15.4 problem 4

Internal problem ID [3208]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 24, page 109
Problem number : 4
Date solved : Monday, January 27, 2025 at 07:26:08 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+4 y^{\prime }&={\mathrm e}^{x}+\sin \left (x \right ) \end{align*}

✓ Solution by Maple

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

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

\[ y = \frac {c_{1} \sin \left (2 x \right )}{2}-\frac {c_2 \cos \left (2 x \right )}{2}+\frac {{\mathrm e}^{x}}{5}-\frac {\cos \left (x \right )}{3}+c_3 \]

✓ Solution by Mathematica

Time used: 0.228 (sec). Leaf size: 37

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

\[ y(x)\to \frac {e^x}{5}-\frac {1}{2} c_2 \cos (2 x)+\cos (x) \left (-\frac {1}{3}+c_1 \sin (x)\right )+c_3 \]