83.14.3 problem 3

Internal problem ID [19111]
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 : 3
Date solved : Monday, March 31, 2025 at 06:48:44 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y&={\mathrm e}^{x}+\sin \left (2 x \right ) \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 33

ode:=diff(diff(y(x),x),x)+4*y(x) = exp(x)+sin(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-x +4 c_1 \right ) \cos \left (2 x \right )}{4}+\frac {\left (1+8 c_2 \right ) \sin \left (2 x \right )}{8}+\frac {{\mathrm e}^{x}}{5} \]

✓ Mathematica. Time used: 0.292 (sec). Leaf size: 41

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

\[ y(x)\to \frac {e^x}{5}+\frac {1}{8} \sin (x) \cos (x)+\left (-\frac {x}{4}+c_1\right ) \cos (2 x)+c_2 \sin (2 x) \]

✓ Sympy. Time used: 0.106 (sec). Leaf size: 24

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

\[ y{\left (x \right )} = C_{2} \sin {\left (2 x \right )} + \left (C_{1} - \frac {x}{4}\right ) \cos {\left (2 x \right )} + \frac {e^{x}}{5} \]