15.11.16 problem 16

Internal problem ID [3126]
Book : Differential Equations by Alfred L. Nelson, Karl W. Folley, Max Coral. 3rd ed. DC heath. Boston. 1964
Section : Exercise 19, page 86
Problem number : 16
Date solved : Monday, January 27, 2025 at 07:22:31 AM
CAS classification : [[_3rd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+4 y^{\prime }-12 y&=x +{\mathrm e}^{2 x} \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 43

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+4*diff(y(x),x)-12*y(x)=x+exp(2*x),y(x), singsol=all)
 

\[ y = \frac {\left (936 c_{1} +18\right ) \cos \left (2 x \right )}{936}+\frac {\left (936 c_3 +27\right ) \sin \left (2 x \right )}{936}+c_2 \,{\mathrm e}^{3 x}-\frac {x}{12}-\frac {{\mathrm e}^{2 x}}{8}-\frac {1}{36} \]

✓ Solution by Mathematica

Time used: 0.426 (sec). Leaf size: 45

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+4*D[y[x],x]-12*y[x]==x+Exp[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{72} \left (-6 x-9 e^{2 x}+72 c_3 e^{3 x}-2\right )+c_1 \cos (2 x)+c_2 \sin (2 x) \]