83.14.1 problem 1

Internal problem ID [19180]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Chapter III. Ordinary linear differential equations with constant coefficients. Exercise III (F) at page 42
Problem number : 1
Date solved : Tuesday, January 28, 2025 at 01:11:30 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\cos \left (2 x \right )+\sin \left (2 x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.005 (sec). Leaf size: 29

dsolve(diff(y(x),x$2)+9*y(x)=cos(2*x)+sin(2*x),y(x), singsol=all)
 

\[ y \left (x \right ) = \sin \left (3 x \right ) c_{2} +\cos \left (3 x \right ) c_{1} +\frac {\cos \left (2 x \right )}{5}+\frac {\sin \left (2 x \right )}{5} \]

✓ Solution by Mathematica

Time used: 0.106 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{5} (\sin (2 x)+\cos (2 x)+5 c_1 \cos (3 x)+5 c_2 \sin (3 x)) \]