83.16.7 problem 7

Internal problem ID [19117]
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 (H) at page 47
Problem number : 7
Date solved : Thursday, March 13, 2025 at 01:43:34 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime }+4 y^{\prime }-12 y&=\left (x -1\right ) {\mathrm e}^{2 x} \end{align*}

✓ Maple. Time used: 0.007 (sec). Leaf size: 29

ode:=diff(diff(y(x),x),x)+4*diff(y(x),x)-12*y(x) = (x-1)*exp(2*x); 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = \frac {\left (\left (x^{2}-\frac {9}{4} x +16 c_{2} \right ) {\mathrm e}^{8 x}+16 c_{1} \right ) {\mathrm e}^{-6 x}}{16} \]

✓ Mathematica. Time used: 0.071 (sec). Leaf size: 38

ode=D[y[x],{x,2}]+4*D[y[x],x]-12*y[x]==(x-1)*Exp[2*x]; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to e^{2 x} \left (\frac {x^2}{16}-\frac {9 x}{64}+\frac {9}{512}+c_2\right )+c_1 e^{-6 x} \]

✓ Sympy. Time used: 0.295 (sec). Leaf size: 26

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x - 1)*exp(2*x) - 12*y(x) + 4*Derivative(y(x), x) + Derivative(y(x), (x, 2)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{2} e^{- 6 x} + \left (C_{1} + \frac {x^{2}}{16} - \frac {9 x}{64}\right ) e^{2 x} \]