15.12.15 problem 15

Internal problem ID [3159]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 20, page 90
Problem number : 15
Date solved : Monday, January 27, 2025 at 07:24:09 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }-4 y^{\prime }&={\mathrm e}^{2 x}+\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 34

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

\[ y = \frac {c_2 \,{\mathrm e}^{4 x}}{4}-{\mathrm e}^{-x} c_{1} +\frac {3 \sin \left (x \right )}{34}-\frac {{\mathrm e}^{2 x}}{12}+\frac {5 \cos \left (x \right )}{34}+c_3 \]

✓ Solution by Mathematica

Time used: 0.285 (sec). Leaf size: 49

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

\[ y(x)\to -\frac {e^{2 x}}{12}+\frac {3 \sin (x)}{34}+\frac {5 \cos (x)}{34}+c_1 \left (-e^{-x}\right )+\frac {1}{4} c_2 e^{4 x}+c_3 \]