87.27.9 problem 15

Internal problem ID [23877]
Book : Ordinary differential equations with modern applications. Ladas, G. E. and Finizio, N. Wadsworth Publishing. California. 1978. ISBN 0-534-00552-7. QA372.F56
Section : Chapter 6. Boundary value problems. Exercise at page 262
Problem number : 15
Date solved : Thursday, October 02, 2025 at 09:46:11 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

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

With initial conditions

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

✓ Maple. Time used: 0.040 (sec). Leaf size: 47

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

\[ y = \frac {\left (-3 x^{3}+3 x \right ) \ln \left (2\right )}{54}+\frac {\ln \left (x \right )}{3}+\frac {4}{9}+\frac {\left (-18 A +4+9 B \right ) x^{3}}{54}+\frac {\left (-9 B -28+72 A \right ) x}{54} \]

✓ Mathematica. Time used: 0.014 (sec). Leaf size: 42

ode=x^2*D[y[x],{x,2}]-3*x*D[y[x],x]+3*y[x]==Log[x]; 
ic={y[1]==A,y[2]==B}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {1}{54} \left (-\left (x^3 (18 A-9 B-4+\log (8))\right )+x (72 A-9 B-28+\log (8))+18 \log (x)+24\right ) \end{align*}

✓ Sympy. Time used: 0.231 (sec). Leaf size: 48

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

\[ y{\left (x \right )} = x^{3} \left (- \frac {A}{3} + \frac {B}{6} - \frac {\log {\left (2 \right )}}{18} + \frac {2}{27}\right ) + x \left (\frac {4 A}{3} - \frac {B}{6} - \frac {14}{27} + \frac {\log {\left (2 \right )}}{18}\right ) + \frac {\log {\left (x \right )}}{3} + \frac {4}{9} \]