20.8.5 problem Problem 5

Internal problem ID [3738]
Book : Differential equations and linear algebra, Stephen W. Goode and Scott A Annin. Fourth edition, 2015
Section : Chapter 8, Linear differential equations of order n. Section 8.4, Complex-Valued Trial Solutions. page 529
Problem number : Problem 5
Date solved : Monday, January 27, 2025 at 07:57:06 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-y^{\prime }-2 y&=40 \sin \left (x \right )^{2} \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 28

dsolve(diff(y(x),x$2)-diff(y(x),x)-2*y(x)=40*sin(x)^2,y(x), singsol=all)
 

\[ y \left (x \right ) = c_{2} {\mathrm e}^{-x}+c_{1} {\mathrm e}^{2 x}-10+\sin \left (2 x \right )+3 \cos \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.070 (sec). Leaf size: 33

DSolve[D[y[x],{x,2}]-D[y[x],x]-2*y[x]==40*Sin[x]^2,y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \sin (2 x)+3 \cos (2 x)+c_1 e^{-x}+c_2 e^{2 x}-10 \]