87.13.18 problem 19

Internal problem ID [23501]
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 2. Linear differential equations. Exercise at page 100
Problem number : 19
Date solved : Thursday, October 02, 2025 at 09:42:31 PM
CAS classification : [[_Emden, _Fowler], [_2nd_order, _linear, `_with_symmetry_[0,F(x)]`]]

\begin{align*} x^{2} y^{\prime \prime }+\frac {7 x y^{\prime }}{2}-\frac {3 y}{2}&=0 \end{align*}

With initial conditions

\begin{align*} y \left (-4\right )&=1 \\ y^{\prime }\left (-4\right )&=0 \\ \end{align*}

✓ Maple. Time used: 0.019 (sec). Leaf size: 16

ode:=x^2*diff(diff(y(x),x),x)+7/2*x*diff(y(x),x)-3/2*y(x) = 0; 
ic:=[y(-4) = 1, D(y)(-4) = 0]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = -\frac {3 i \sqrt {x}}{7}-\frac {64}{7 x^{3}} \]

✓ Mathematica. Time used: 0.009 (sec). Leaf size: 23

ode=x^2*D[y[x],{x,2}]+7/2*x*D[y[x],x]-3/2*y[x]==0; 
ic={y[-4]==1,Derivative[1][y][-4] ==0}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to -\frac {64+3 i x^{7/2}}{7 x^3} \end{align*}

✓ Sympy. Time used: 0.121 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), (x, 2)) + 7*x*Derivative(y(x), x)/2 - 3*y(x)/2,0) 
ics = {y(-4): 1, Subs(Derivative(y(x), x), x, -4): 0} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = - \frac {3 i \sqrt {x}}{7} - \frac {64}{7 x^{3}} \]