71.11.6 problem 6

Internal problem ID [14515]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.4, page 218
Problem number : 6
Date solved : Tuesday, January 28, 2025 at 06:42:53 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }+y^{\prime \prime }-y^{\prime }-y&=\left (2 x^{2}+4 x +8\right ) \cos \left (x \right )+\left (6 x^{2}+8 x +12\right ) \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.007 (sec). Leaf size: 43

dsolve(diff(y(x),x$3)+diff(y(x),x$2)-diff(y(x),x)-y(x)=(2*x^2+4*x+8)*cos(x)+(6*x^2+8*x+12)*sin(x),y(x), singsol=all)
 

\[ y = \left (c_{3} x +c_{2} \right ) {\mathrm e}^{-x}+\left (x^{2}-6 x -2\right ) \cos \left (x \right )+\left (-2 x^{2}-4 x +1\right ) \sin \left (x \right )+{\mathrm e}^{x} c_{1} \]

✓ Solution by Mathematica

Time used: 0.010 (sec). Leaf size: 55

DSolve[D[y[x],{x,3}]+D[y[x],{x,2}]-D[y[x],x]-y[x]==(2*x^2+4*x+8)*Cos[x]+(6*x^2+8*x+12)*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to \left (x^2-6 x-2\right ) \cos (x)+e^{-x} \left (-e^x \left (2 x^2+4 x-1\right ) \sin (x)+c_2 x+c_3 e^{2 x}+c_1\right ) \]