83.44.15 problem Ex 15 page 49

Internal problem ID [19472]
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 15 page 49
Date solved : Monday, March 31, 2025 at 07:19:40 PM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

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

✓ Maple. Time used: 0.003 (sec). Leaf size: 24

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

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

✓ Mathematica. Time used: 0.016 (sec). Leaf size: 32

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

\[ y(x)\to -\frac {\sin (x)}{2}+\frac {1}{2} (x+1) \cos (x)+e^x (c_2 x+c_1) \]

✓ Sympy. Time used: 0.220 (sec). Leaf size: 27

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

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