68.15.32 problem 32

Internal problem ID [17758]
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 : 32
Date solved : Thursday, October 02, 2025 at 02:27:48 PM
CAS classification : [[_Emden, _Fowler]]

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

With initial conditions

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

✓ Maple. Time used: 0.057 (sec). Leaf size: 13

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

\[ y = \frac {4 x^{{7}/{2}}}{5}-\frac {9 x}{5} \]

✓ Mathematica. Time used: 0.008 (sec). Leaf size: 19

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

\begin{align*} y(x)&\to \frac {1}{5} x \left (4 x^{5/2}-9\right ) \end{align*}

✓ Sympy. Time used: 0.102 (sec). Leaf size: 15

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

\[ y{\left (x \right )} = \frac {4 x^{\frac {7}{2}}}{5} - \frac {9 x}{5} \]