83.17.11 problem 11

Internal problem ID [19207]
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. Misc. Examples on chapter III at page 50
Problem number : 11
Date solved : Tuesday, January 28, 2025 at 01:13:30 PM
CAS classification : [[_high_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime \prime }+10 y^{\prime \prime }+9 y&=96 \sin \left (2 x \right ) \cos \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.004 (sec). Leaf size: 41

dsolve(diff(y(x),x$4)+10*diff(y(x),x$2)+9*y(x)=96*sin(2*x)*cos(x),y(x), singsol=all)
 

\[ y \left (x \right ) = \left (x +c_3 \right ) \cos \left (3 x \right )+\frac {\left (12 c_4 -11\right ) \sin \left (3 x \right )}{12}+\left (-3 x +c_{1} \right ) \cos \left (x \right )+\frac {\sin \left (x \right ) \left (2 c_{2} -3\right )}{2} \]

✓ Solution by Mathematica

Time used: 0.081 (sec). Leaf size: 50

DSolve[D[y[x],{x,4}]+10*D[y[x],{x,2}]+9*y[x]==96*Sin[2*x]*Cos[x],y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\frac {3 \sin (x)}{2}-\frac {7}{6} \sin (3 x)+(-3 x+c_3) \cos (x)+(x+c_1) \cos (3 x)+c_4 \sin (x)+c_2 \sin (3 x) \]