83.49.22 problem Ex 22 page 138

Internal problem ID [19556]
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 22 page 138
Date solved : Thursday, March 13, 2025 at 02:49:26 PM
CAS classification : [[_2nd_order, _exact, _linear, _nonhomogeneous]]

\begin{align*} x^{2} y^{\prime \prime }+x y^{\prime }-y&=x^{2} {\mathrm e}^{x} \end{align*}

✓ Maple. Time used: 0.002 (sec). Leaf size: 21

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

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

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

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

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

✓ Sympy. Time used: 0.527 (sec). Leaf size: 17

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

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