89.2.25 problem 27

Internal problem ID [24290]
Book : A short course in Differential Equations. Earl D. Rainville. Second edition. 1958. Macmillan Publisher, NY. CAT 58-5010
Section : Chapter 2. Equations of the first order and first degree. Exercises at page 27
Problem number : 27
Date solved : Thursday, October 02, 2025 at 10:07:41 PM
CAS classification : [[_homogeneous, `class A`], _rational, _Riccati]

\begin{align*} y^{2}+7 y x +16 x^{2}+x^{2} y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.026 (sec). Leaf size: 20

ode:=y(x)^2+7*x*y(x)+16*x^2+x^2*diff(y(x),x) = 0; 
ic:=[y(1) = 1]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \frac {x \left (1-20 \ln \left (x \right )\right )}{1+5 \ln \left (x \right )} \]

✓ Mathematica. Time used: 0.098 (sec). Leaf size: 21

ode=( y[x]^2+7*x*y[x]+16*x^2 )+(x^2 )*D[y[x],x]==0; 
ic={y[1]==1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to \frac {x-20 x \log (x)}{5 \log (x)+1} \end{align*}

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(x**2*Derivative(y(x), x) + 16*x**2 + 7*x*y(x) + y(x)**2,0) 
ics = {y(1): 1} 
dsolve(ode,func=y(x),ics=ics)
 

ValueError : Couldnt solve for initial conditions