12.19.49 problem section 9.3, problem 49

Internal problem ID [2196]
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 49
Date solved : Monday, January 27, 2025 at 05:43:23 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-y^{\prime \prime }+y^{\prime }-y&=5 \,{\mathrm e}^{2 x}+2 \,{\mathrm e}^{x}-4 \cos \left (x \right )+4 \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 31

dsolve(1*diff(y(x),x$3)-1*diff(y(x),x$2)+1*diff(y(x),x)-1*y(x)=5*exp(2*x)+2*exp(x)-4*cos(x)+4*sin(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{2 x}+\left (2 x +c_1 +2\right ) \cos \left (x \right )+\left (x +c_2 -1\right ) {\mathrm e}^{x}+\left (c_3 -2\right ) \sin \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.253 (sec). Leaf size: 35

DSolve[1*D[y[x],{x,3}]-1*D[y[x],{x,2}]+1*D[y[x],x]-1*y[x]==5*Exp[2*x]+2*Exp[x]-4*Cos[x]+4*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^x \left (x+e^x-1+c_3\right )+(2 x+1+c_1) \cos (x)+(-2+c_2) \sin (x) \]