85.55.2 problem 3

Internal problem ID [22825]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. C Exercises at page 197
Problem number : 3
Date solved : Thursday, October 02, 2025 at 09:15:01 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 36

ode:=diff(diff(y(x),x),x)+4*y(x) = sin(x)^4; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {3}{32}+\frac {\left (-1+12 c_1 \right ) \cos \left (2 x \right )}{12}+\frac {\left (-x +8 c_2 \right ) \sin \left (2 x \right )}{8}-\frac {\cos \left (4 x \right )}{96} \]

✓ Mathematica. Time used: 0.055 (sec). Leaf size: 43

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

\begin{align*} y(x)&\to \frac {1}{96} (-12 x \sin (2 x)-\cos (4 x)+(-8+96 c_1) \cos (2 x)+96 c_2 \sin (2 x)+9) \end{align*}

✓ Sympy. Time used: 1.176 (sec). Leaf size: 61

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(4*y(x) - sin(x)**4 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sin {\left (2 x \right )} + C_{2} \cos {\left (2 x \right )} - \frac {x \sin {\left (x \right )} \cos {\left (x \right )}}{4} + \frac {\sin ^{8}{\left (x \right )}}{4} - \frac {3 \sin ^{6}{\left (x \right )}}{4} + \frac {2 \sin ^{4}{\left (x \right )}}{3} + \frac {\sin ^{2}{\left (x \right )} \cos ^{6}{\left (x \right )}}{4} \]