83.47.6 problem Ex 6 page 86

Internal problem ID [19504]
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 VI. Homogeneous linear equations with variable coefficients
Problem number : Ex 6 page 86
Date solved : Thursday, March 13, 2025 at 02:42:59 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} x^{2} y^{\prime \prime }-3 x y^{\prime }+4 y&=2 x^{2} \end{align*}

✓ Maple. Time used: 0.006 (sec). Leaf size: 18

ode:=x^2*diff(diff(y(x),x),x)-3*x*diff(y(x),x)+4*y(x) = 2*x^2; 
dsolve(ode,y(x), singsol=all);
 

\[ y \left (x \right ) = x^{2} \left (c_{2} +\ln \left (x \right ) c_{1} +\ln \left (x \right )^{2}\right ) \]

✓ Mathematica. Time used: 0.021 (sec). Leaf size: 22

ode=x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+4*y[x]==2*x^2; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to x^2 \left (\log ^2(x)+2 c_2 \log (x)+c_1\right ) \]

✓ Sympy. Time used: 0.258 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) - 2*x**2 - 3*x*Derivative(y(x), x) + 4*y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

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