67.2.27 problem Problem 5(a)

Internal problem ID [13913]
Book : APPLIED DIFFERENTIAL EQUATIONS The Primary Course by Vladimir A. Dobrushkin. CRC Press 2015
Section : Chapter 4, Second and Higher Order Linear Differential Equations. Problems page 221
Problem number : Problem 5(a)
Date solved : Monday, March 31, 2025 at 08:17:52 AM
CAS classification : [[_2nd_order, _linear, _nonhomogeneous]]

\begin{align*} \left (x -3\right ) y^{\prime \prime }+\ln \left (x \right ) y&=x^{2} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=1\\ y^{\prime }\left (1\right )&=2 \end{align*}

✗ Maple

ode:=(x-3)*diff(diff(y(x),x),x)+ln(x)*y(x) = x^2; 
ic:=y(1) = 1, D(y)(1) = 2; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ \text {No solution found} \]

✗ Mathematica

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

Not solved

✗ Sympy

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

NotImplementedError : solve: Cannot solve -x**2 + (x - 3)*Derivative(y(x), (x, 2)) + y(x)*log(x)