83.17.10 problem 10

Internal problem ID [19135]
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 : 10
Date solved : Monday, March 31, 2025 at 06:49:26 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 36

ode:=diff(diff(y(x),x),x)+y(x) = 3*cos(x)^2+2*sin(x)^3; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (\sin \left (x \right )-4\right ) \cos \left (x \right )^{2}}{4}+\frac {\left (4 c_1 -3 x \right ) \cos \left (x \right )}{4}+2+\frac {\left (4 c_2 +2\right ) \sin \left (x \right )}{4} \]

✓ Mathematica. Time used: 0.151 (sec). Leaf size: 43

ode=D[y[x],{x,2}]+y[x]==3*Cos[x]^2+2*Sin[x]^3; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{16} (2 \sin (x)+\sin (3 x)-8 \cos (2 x)-4 (3 x-4 c_1) \cos (x)+16 c_2 \sin (x)+24) \]

✓ Sympy. Time used: 0.661 (sec). Leaf size: 49

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(y(x) - 2*sin(x)**3 - 3*cos(x)**2 + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} \sin {\left (x \right )} - \frac {\left (1 - \cos {\left (2 x \right )}\right )^{2}}{4} + \left (C_{1} - \frac {3 x}{4}\right ) \cos {\left (x \right )} + \frac {\sin {\left (3 x \right )}}{16} - \cos {\left (2 x \right )} + \frac {\cos {\left (4 x \right )}}{8} + \frac {15}{8} \]