83.17.4 problem 4

Internal problem ID [19129]
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. Misc. Examples on chapter III at page 50
Problem number : 4
Date solved : Monday, March 31, 2025 at 06:49:11 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.004 (sec). Leaf size: 21

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

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

✓ Mathematica. Time used: 0.02 (sec). Leaf size: 25

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

\[ y(x)\to e^x (-x \sin (x)-2 \cos (x)+c_2 x+c_1) \]

✓ Sympy. Time used: 0.262 (sec). Leaf size: 19

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

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