65.9.2 problem 16.1 (ii)

Internal problem ID [13781]
Book : AN INTRODUCTION TO ORDINARY DIFFERENTIAL EQUATIONS by JAMES C. ROBINSON. Cambridge University Press 2004
Section : Chapter 16, Higher order linear equations with constant coefficients. Exercises page 153
Problem number : 16.1 (ii)
Date solved : Tuesday, January 28, 2025 at 06:03:24 AM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-3 y^{\prime \prime }+2 y&=\sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.006 (sec). Leaf size: 38

dsolve(diff(y(x),x$3)-3*diff(y(x),x$2)+2*y(x)=sin(x),y(x), singsol=all)
 

\[ y = {\mathrm e}^{x} c_{1} +c_{2} {\mathrm e}^{\left (1+\sqrt {3}\right ) x}+c_{3} {\mathrm e}^{-\left (\sqrt {3}-1\right ) x}+\frac {\cos \left (x \right )}{26}+\frac {5 \sin \left (x \right )}{26} \]

✓ Solution by Mathematica

Time used: 0.101 (sec). Leaf size: 143

DSolve[D[y[x],{x,3}]-3*D[y[x],{x,2}]+2*y[x]==Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to e^{x-\sqrt {3} x} \int _1^x\frac {1}{6} e^{\left (-1+\sqrt {3}\right ) K[1]} \sin (K[1])dK[1]+e^{\left (1+\sqrt {3}\right ) x} \int _1^x\frac {1}{6} e^{-\left (\left (1+\sqrt {3}\right ) K[2]\right )} \sin (K[2])dK[2]+e^x \int _1^x-\frac {1}{3} e^{-K[3]} \sin (K[3])dK[3]+c_1 e^{x-\sqrt {3} x}+c_2 e^{\left (1+\sqrt {3}\right ) x}+c_3 e^x \]