68.5.16 problem 16

Internal problem ID [17267]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Exercises 2.3, page 49
Problem number : 16
Date solved : Thursday, October 02, 2025 at 02:00:24 PM
CAS classification : [_linear]

\begin{align*} y^{\prime }-\frac {9 x y}{9 x^{2}+49}&=x \end{align*}

✓ Maple. Time used: 0.001 (sec). Leaf size: 20

ode:=diff(y(x),x)-9*x/(9*x^2+49)*y(x) = x; 
dsolve(ode,y(x), singsol=all);
 

\[ y = x^{2}+\frac {49}{9}+\sqrt {9 x^{2}+49}\, c_1 \]

✓ Mathematica. Time used: 0.024 (sec). Leaf size: 26

ode=D[y[x],x]-9*x/(9*x^2+49)*y[x]==x; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\begin{align*} y(x)&\to x^2+c_1 \sqrt {9 x^2+49}+\frac {49}{9} \end{align*}

✓ Sympy. Time used: 0.259 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-x - 9*x*y(x)/(9*x**2 + 49) + Derivative(y(x), x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = C_{1} \sqrt {9 x^{2} + 49} + x^{2} + \frac {49}{9} \]