12.19.48 problem section 9.3, problem 48

Internal problem ID [2195]
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 48
Date solved : Monday, January 27, 2025 at 05:43:23 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

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

✓ Solution by Maple

Time used: 0.010 (sec). Leaf size: 34

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

\[ y = \left (c_2 +x -2\right ) {\mathrm e}^{2 x}+\left (2 x^{2}+\left (c_3 +4\right ) x +c_1 +4\right ) {\mathrm e}^{x}-\cos \left (x \right ) \]

✓ Solution by Mathematica

Time used: 0.252 (sec). Leaf size: 38

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

\[ y(x)\to -\cos (x)+e^x \left (2 x^2+(4+c_2) x+e^x (x-2+c_3)+4+c_1\right ) \]