15.11.24 problem 24

Internal problem ID [3134]
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 : 24
Date solved : Monday, January 27, 2025 at 07:23:01 AM
CAS classification : [[_3rd_order, _missing_y]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }&=\left (2 x^{2}+x \right ) {\mathrm e}^{-2 x}+5 \cos \left (3 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 45

dsolve(diff(y(x),x$3)+2*diff(y(x),x$2)=(2*x^2+x)*exp(-2*x)+5*cos(3*x),y(x), singsol=all)
 

\[ y = \frac {\left (8 x^{3}+30 x^{2}+12 c_{1} +48 x +33\right ) {\mathrm e}^{-2 x}}{48}+c_2 x +c_3 -\frac {10 \cos \left (3 x \right )}{117}-\frac {5 \sin \left (3 x \right )}{39} \]

✓ Solution by Mathematica

Time used: 0.985 (sec). Leaf size: 56

DSolve[D[y[x],{x,3}]+2*D[y[x],{x,2}]==(2*x^2+x)*Exp[-2*x]+5*Cos[3*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \frac {1}{48} e^{-2 x} \left (8 x^3+30 x^2+48 x+33+12 c_1\right )-\frac {5}{39} \sin (3 x)-\frac {10}{117} \cos (3 x)+c_3 x+c_2 \]