15.15.13 problem 14

Internal problem ID [3217]
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 : 14
Date solved : Monday, January 27, 2025 at 07:26:20 AM
CAS classification : [[_2nd_order, _missing_y]]

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

Solution by Maple

Time used: 0.003 (sec). Leaf size: 54

dsolve(diff(y(x),x$2)+2*diff(y(x),x)=x^3*sin(2*x),y(x), singsol=all)
 
\[ y = \frac {\left (-8 x^{3}+24 x^{2}+6 x -15\right ) \sin \left (2 x \right )}{64}+\frac {\left (-4 x^{3}-6 x^{2}+15 x \right ) \cos \left (2 x \right )}{32}-\frac {{\mathrm e}^{-2 x} c_{1}}{2}+c_2 \]

Solution by Mathematica

Time used: 0.502 (sec). Leaf size: 61

DSolve[D[y[x],{x,2}]+2*D[y[x],x]==x^3*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 
\[ y(x)\to -\frac {1}{32} x \left (4 x^2+6 x-15\right ) \cos (2 x)+\frac {1}{64} \left (-8 x^3+24 x^2+6 x-15\right ) \sin (2 x)-\frac {1}{2} c_1 e^{-2 x}+c_2 \]