12.19.52 problem section 9.3, problem 52

Internal problem ID [2199]
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 52
Date solved : Monday, January 27, 2025 at 05:43:27 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+3 y^{\prime \prime }+3 y^{\prime }+y&=12 \,{\mathrm e}^{-x}+9 \cos \left (2 x \right )-13 \sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 35

dsolve(1*diff(y(x),x$3)+3*diff(y(x),x$2)+3*diff(y(x),x)+y(x)=12*exp(-x)+9*cos(2*x)-13*sin(2*x),y(x), singsol=all)
 

\[ y = \left (c_3 \,x^{2}+2 x^{3}+c_2 x +c_1 \right ) {\mathrm e}^{-x}-\cos \left (2 x \right )+\sin \left (2 x \right ) \]

✓ Solution by Mathematica

Time used: 0.250 (sec). Leaf size: 46

DSolve[1*D[y[x],{x,3}]+3*D[y[x],{x,2}]+3*D[y[x],x]+1*y[x]==12*Exp[-x]+9*Cos[2*x]-13*Sin[2*x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{-x} \left (2 x^3+c_3 x^2+e^x \sin (2 x)-e^x \cos (2 x)+c_2 x+c_1\right ) \]