83.49.13 problem Ex 13 page 130

Internal problem ID [19555]
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 VIII. Linear equations of second order
Problem number : Ex 13 page 130
Date solved : Monday, March 31, 2025 at 07:33:14 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }-\left (8 \,{\mathrm e}^{2 x}+2\right ) y^{\prime }+4 \,{\mathrm e}^{4 x} y&={\mathrm e}^{6 x} \end{align*}

✓ Maple. Time used: 0.138 (sec). Leaf size: 39

ode:=diff(diff(y(x),x),x)-(8*exp(2*x)+2)*diff(y(x),x)+4*exp(4*x)*y(x) = exp(6*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = {\mathrm e}^{{\mathrm e}^{2 x} \left (2+\sqrt {3}\right )} c_2 +{\mathrm e}^{-{\mathrm e}^{2 x} \left (\sqrt {3}-2\right )} c_1 +\frac {{\mathrm e}^{2 x}}{4}+1 \]

✓ Mathematica. Time used: 0.283 (sec). Leaf size: 53

ode=D[y[x],{x,2}]-(8*Exp[2*x]+2)*D[y[x],x]+4*Exp[4*x]*y[x]==Exp[6*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {e^{2 x}}{4}+c_1 e^{-\left (\left (\sqrt {3}-2\right ) e^{2 x}\right )}+c_2 e^{\left (2+\sqrt {3}\right ) e^{2 x}}+1 \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq((-8*exp(2*x) - 2)*Derivative(y(x), x) + 4*y(x)*exp(4*x) - exp(6*x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

NotImplementedError : The given ODE Derivative(y(x), x) - (4*y(x)*exp(4*x) - exp(6*x) + Derivative(y(x), (x, 2)))/(2*(4*exp(2*x) + 1)) cannot be solved by the factorable group method