85.64.8 problem 1 (h)

Internal problem ID [22875]
Book : Applied Differential Equations. By Murray R. Spiegel. 3rd edition. 1980. Pearson. ISBN 978-0130400970
Section : Chapter 4. Linear differential equations. A Exercises at page 213
Problem number : 1 (h)
Date solved : Thursday, October 02, 2025 at 09:16:06 PM
CAS classification : [[_2nd_order, _with_linear_symmetries]]

\begin{align*} y^{\prime \prime }&=\frac {\frac {4 x}{25}-\frac {4 y}{25}}{x^{2}} \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=0 \\ y^{\prime }\left (1\right )&=2 \\ \end{align*}

✓ Maple. Time used: 0.025 (sec). Leaf size: 16

ode:=diff(diff(y(x),x),x) = 4/25*(x-y(x))/x^2; 
ic:=[y(1) = 0, D(y)(1) = 2]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = 2 x^{{4}/{5}}-3 x^{{1}/{5}}+x \]

✓ Mathematica. Time used: 0.012 (sec). Leaf size: 21

ode=D[y[x],{x,2}]==4/25*( (x-y[x])/x^2); 
ic={y[1]==0,Derivative[1][y][1] ==2}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to 2 x^{4/5}+x-3 \sqrt [5]{x} \end{align*}

✓ Sympy. Time used: 0.205 (sec). Leaf size: 17

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), (x, 2)) - 4*(x - y(x))/(25*x**2),0) 
ics = {y(1): 0, Subs(Derivative(y(x), x), x, 1): 2} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 2 x^{\frac {4}{5}} - 3 \sqrt [5]{x} + x \]