71.9.4 problem 4

Internal problem ID [14412]
Book : Ordinary Differential Equations by Charles E. Roberts, Jr. CRC Press. 2010
Section : Chapter 4. N-th Order Linear Differential Equations. Exercises 4.1, page 186
Problem number : 4
Date solved : Monday, March 31, 2025 at 12:26:24 PM
CAS classification : [[_2nd_order, _missing_y]]

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

With initial conditions

\begin{align*} y \left (5\right )&=0\\ y^{\prime }\left (5\right )&=1 \end{align*}

✓ Maple. Time used: 0.050 (sec). Leaf size: 24

ode:=x*(x-3)*diff(diff(y(x),x),x)+3*diff(y(x),x) = x^2; 
ic:=y(5) = 0, D(y)(5) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {x^{2}}{2}-\frac {8 x}{5}-\frac {24 \ln \left (x -3\right )}{5}+\frac {24 \ln \left (2\right )}{5}-\frac {9}{2} \]

✓ Mathematica. Time used: 3.746 (sec). Leaf size: 325

ode=x*(x-3)*D[y[x],{x,2}]+3*D[y[x],x]==x^2; 
ic={y[5]==0,Derivative[1][y][5]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \int _1^x\exp \left (\int _1^{K[3]}-\frac {3}{(K[1]-3) K[1]}dK[1]-\int _1^5-\frac {3}{(K[1]-3) K[1]}dK[1]\right ) \left (-\exp \left (\int _1^5-\frac {3}{(K[1]-3) K[1]}dK[1]\right ) \int _1^5\frac {\exp \left (-\int _1^{K[2]}-\frac {3}{(K[1]-3) K[1]}dK[1]\right ) K[2]}{K[2]-3}dK[2]+\exp \left (\int _1^5-\frac {3}{(K[1]-3) K[1]}dK[1]\right ) \int _1^{K[3]}\frac {\exp \left (-\int _1^{K[2]}-\frac {3}{(K[1]-3) K[1]}dK[1]\right ) K[2]}{K[2]-3}dK[2]+1\right )dK[3]-\int _1^5\exp \left (\int _1^{K[3]}-\frac {3}{(K[1]-3) K[1]}dK[1]\right ) \left (-\int _1^5\frac {\exp \left (-\int _1^{K[2]}-\frac {3}{(K[1]-3) K[1]}dK[1]\right ) K[2]}{K[2]-3}dK[2]+\exp \left (-\int _1^5-\frac {3}{(K[1]-3) K[1]}dK[1]\right )+\int _1^{K[3]}\frac {\exp \left (-\int _1^{K[2]}-\frac {3}{(K[1]-3) K[1]}dK[1]\right ) K[2]}{K[2]-3}dK[2]\right )dK[3] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x**2 + x*(x - 3)*Derivative(y(x), (x, 2)) + 3*Derivative(y(x), x),0) 
ics = {y(5): 0, Subs(Derivative(y(x), x), x, 5): 1} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out