12.19.73 problem section 9.3, problem 73

Internal problem ID [2220]
Book : Elementary differential equations with boundary value problems. William F. Trench. Brooks/Cole 2001
Section : Chapter 9 Introduction to Linear Higher Order Equations. Section 9.3. Undetermined Coefficients for Higher Order Equations. Page 495
Problem number : section 9.3, problem 73
Date solved : Monday, January 27, 2025 at 05:43:42 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+2 y^{\prime \prime }+y^{\prime }+2 y&=30 \cos \left (x \right )-10 \sin \left (x \right ) \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=3\\ y^{\prime }\left (0\right )&=-4\\ y^{\prime \prime }\left (0\right )&=16 \end{align*}

✓ Solution by Maple

Time used: 0.021 (sec). Leaf size: 25

dsolve([0*diff(y(x),x$4)+1*diff(y(x),x$3)+2*diff(y(x),x$2)+1*diff(y(x),x)+2*y(x)=30*cos(x)-10*sin(x),y(0) = 3, D(y)(0) = -4, (D@@2)(y)(0) = 16],y(x), singsol=all)
 

\[ y = {\mathrm e}^{-2 x}+\left (-x +2\right ) \cos \left (x \right )+\left (7 x -1\right ) \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.085 (sec). Leaf size: 26

DSolve[{0*D[y[x],{x,4}]+1*D[y[x],{x,3}]+2*D[y[x],{x,2}]+1*D[y[x],x]+2*y[x]==30*Cos[x]-10*Sin[x],{y[0]==3,Derivative[1][y][0] ==-4,Derivative[2][y][0] ==16}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-2 x}+(7 x-1) \sin (x)-((x-2) \cos (x)) \]