83.16.5 problem 5

Internal problem ID [19123]
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 : 5
Date solved : Monday, March 31, 2025 at 06:49:01 PM
CAS classification : [[_3rd_order, _linear, _nonhomogeneous]]

\begin{align*} y^{\prime \prime \prime }-7 y^{\prime }-6 y&={\mathrm e}^{2 x} \left (1+x \right ) \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 34

ode:=diff(diff(diff(y(x),x),x),x)-7*diff(y(x),x)-6*y(x) = exp(2*x)*(1+x); 
dsolve(ode,y(x), singsol=all);
 

\[ y = \frac {\left (-12 x -17\right ) {\mathrm e}^{2 x}}{144}+c_1 \,{\mathrm e}^{-2 x}+c_2 \,{\mathrm e}^{-x}+c_3 \,{\mathrm e}^{3 x} \]

✓ Mathematica. Time used: 0.006 (sec). Leaf size: 44

ode=D[y[x],{x,3}]-7*D[y[x],x]-6*y[x]==Exp[2*x]*(1+x); 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to -\frac {1}{144} e^{2 x} (12 x+17)+c_1 e^{-2 x}+c_2 e^{-x}+c_3 e^{3 x} \]

✓ Sympy. Time used: 0.280 (sec). Leaf size: 34

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-(x + 1)*exp(2*x) - 6*y(x) - 7*Derivative(y(x), x) + Derivative(y(x), (x, 3)),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} e^{- 2 x} + C_{2} e^{- x} + C_{3} e^{3 x} + \frac {\left (- 12 x - 17\right ) e^{2 x}}{144} \]