20.7.11 problem Problem 35

Internal problem ID [3726]
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 8.3, The Method of Undetermined Coefficients. page 525
Problem number : Problem 35
Date solved : Monday, January 27, 2025 at 07:56:20 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+y^{\prime }-2 y&=-10 \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=2\\ y^{\prime }\left (0\right )&=1 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 15

dsolve([diff(y(x),x$2)+diff(y(x),x)-2*y(x)=-10*sin(x),y(0) = 2, D(y)(0) = 1],y(x), singsol=all)
 

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

✓ Solution by Mathematica

Time used: 0.017 (sec). Leaf size: 17

DSolve[{D[y[x],{x,2}]+D[y[x],x]-2*y[x]==-10*Sin[x],{y[0]==2,Derivative[1][y][0] ==1}},y[x],x,IncludeSingularSolutions -> True]
 

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