83.44.13 problem Ex 13 page 47

Internal problem ID [19470]
Book : A Text book for differentional equations for postgraduate students by Ray and Chaturvedi. First edition, 1958. BHASKAR press. INDIA
Section : Book Solved Excercises. Chapter III. Ordinary linear differential equations with constant coefficients
Problem number : Ex 13 page 47
Date solved : Monday, March 31, 2025 at 07:19:37 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 33

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

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

✓ Mathematica. Time used: 0.07 (sec). Leaf size: 34

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

\[ y(x)\to \frac {1}{16} e^{-2 x} \left (-8 x^2+e^{4 x}+16 c_2 x+16 c_1\right ) \]

✗ Sympy

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

NotImplementedError : The given ODE y(x) - sinh(2*x)/2 + Derivative(y(x), x) + Derivative(y(x), (x, 2))/4 cannot be solved by the factorable group method