15.12.9 problem 9

Internal problem ID [3153]
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 : 9
Date solved : Monday, January 27, 2025 at 07:24:00 AM
CAS classification : [[_3rd_order, _missing_y]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 39

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

\[ y = {\mathrm e}^{-4 x} \left (\left (c_3 -\frac {3 \cos \left (2 x \right )}{100}-\frac {\sin \left (2 x \right )}{25}-\frac {3}{100}\right ) {\mathrm e}^{4 x}+{\mathrm e}^{5 x} c_{1} -\frac {c_2}{4}\right ) \]

✓ Solution by Mathematica

Time used: 0.333 (sec). Leaf size: 41

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

\[ y(x)\to -\frac {1}{25} \sin (2 x)-\frac {3}{100} \cos (2 x)-\frac {1}{4} c_1 e^{-4 x}+c_2 e^x+c_3 \]