74.15.31 problem 31

Internal problem ID [16399]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 4. Higher Order Equations. Exercises 4.7, page 195
Problem number : 31
Date solved : Monday, March 31, 2025 at 02:52:12 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} 3 x^{2} y^{\prime \prime }-4 x y^{\prime }+2 y&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.053 (sec). Leaf size: 15

ode:=3*x^2*diff(diff(y(x),x),x)-4*x*diff(y(x),x)+2*y(x) = 0; 
ic:=y(1) = 2, D(y)(1) = 1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = \frac {x^{2}}{5}+\frac {9 x^{{1}/{3}}}{5} \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 20

ode=3*x^2*D[y[x],{x,2}]-4*x*D[y[x],x]+2*y[x]==0; 
ic={y[1]==2,Derivative[1][y][1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to \frac {1}{5} \left (x^2+9 \sqrt [3]{x}\right ) \]

✓ Sympy. Time used: 0.169 (sec). Leaf size: 15

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(3*x**2*Derivative(y(x), (x, 2)) - 4*x*Derivative(y(x), x) + 2*y(x),0) 
ics = {y(1): 2, Subs(Derivative(y(x), x), x, 1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {9 \sqrt [3]{x}}{5} + \frac {x^{2}}{5} \]