89.2.31 problem 33

Internal problem ID [24296]
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 : 33
Date solved : Thursday, October 02, 2025 at 10:10:11 PM
CAS classification : [[_homogeneous, `class A`], _rational, [_Abel, `2nd type`, `class A`]]

\begin{align*} 16 x +15 y+\left (3 x +y\right ) y^{\prime }&=0 \end{align*}

With initial conditions

\begin{align*} y \left (1\right )&=-3 \\ \end{align*}

✓ Maple. Time used: 1.283 (sec). Leaf size: 77

ode:=16*x+15*y(x)+(3*x+y(x))*diff(y(x),x) = 0; 
ic:=[y(1) = -3]; 
dsolve([ode,op(ic)],y(x), singsol=all);
 

\[ y = \operatorname {RootOf}\left (12 \sqrt {65}\, \operatorname {arctanh}\left (\frac {\left (\textit {\_Z} +9 x \right ) \sqrt {65}}{65 x}\right )-6 \sqrt {65}\, \ln \left (101+12 \sqrt {65}\right )+6 \sqrt {65}\, \ln \left (29\right )-65 i \pi +130 \ln \left (x \right )+65 \ln \left (\frac {\textit {\_Z}^{2}+18 \textit {\_Z} x +16 x^{2}}{x^{2}}\right )-65 \ln \left (29\right )\right ) \]

✓ Mathematica. Time used: 0.075 (sec). Leaf size: 120

ode=( 16*x+15*y[x] )+( 3*x+y[x] )*D[y[x],x]==0; 
ic={y[1]==-3}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\frac {1}{130} \left (65-6 \sqrt {65}\right ) \log \left (-\frac {y(x)}{x}+\sqrt {65}-9\right )+\frac {1}{130} \left (65+6 \sqrt {65}\right ) \log \left (\frac {y(x)}{x}+\sqrt {65}+9\right )=\frac {1}{130} \left (65 \log \left (\sqrt {65}-6\right )-6 \sqrt {65} \log \left (\sqrt {65}-6\right )+65 \log \left (6+\sqrt {65}\right )+6 \sqrt {65} \log \left (6+\sqrt {65}\right )\right )-\log (x),y(x)\right ] \]

✗ Sympy

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(16*x + (3*x + y(x))*Derivative(y(x), x) + 15*y(x),0) 
ics = {y(1): -3} 
dsolve(ode,func=y(x),ics=ics)
 

Timed Out