8.11.22 problem 45

Internal problem ID [890]
Book : Differential equations and linear algebra, 3rd ed., Edwards and Penney
Section : Section 5.5, Nonhomogeneous equations and undetermined coefficients Page 351
Problem number : 45
Date solved : Wednesday, February 05, 2025 at 04:43:29 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+9 y&=\sin \left (x \right )^{4} \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 32

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

\[ y = \sin \left (3 x \right ) c_2 +\cos \left (3 x \right ) c_1 -\frac {\cos \left (2 x \right )}{10}-\frac {\cos \left (2 x \right )^{2}}{28}+\frac {5}{84} \]

✓ Solution by Mathematica

Time used: 0.043 (sec). Leaf size: 39

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

\[ y(x)\to -\frac {1}{10} \cos (2 x)-\frac {1}{56} \cos (4 x)+c_1 \cos (3 x)+c_2 \sin (3 x)+\frac {1}{24} \]