23.3.16 problem 8(f)

Internal problem ID [4157]
Book : Theory and solutions of Ordinary Differential equations, Donald Greenspan, 1960
Section : Chapter 4. The general linear differential equation of order n. Exercises at page 63
Problem number : 8(f)
Date solved : Monday, January 27, 2025 at 08:40:55 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.003 (sec). Leaf size: 40

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

\[ y \left (x \right ) = \frac {\left (-30 x +7\right ) \cos \left (2 x \right )}{200}+\frac {\left (12-5 x \right ) \sin \left (2 x \right )}{100}-{\mathrm e}^{-2 x} c_{1} +c_{2} {\mathrm e}^{-x} \]

✓ Solution by Mathematica

Time used: 0.024 (sec). Leaf size: 48

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

\[ y(x)\to c_1 e^{-2 x}+c_2 e^{-x}+\frac {1}{200} (2 (12-5 x) \sin (2 x)+(7-30 x) \cos (2 x)) \]