34.3.19 problem 25 (d)

Internal problem ID [7910]
Book : Schaums Outline. Theory and problems of Differential Equations, 1st edition. Frank Ayres. McGraw Hill 1952
Section : Chapter 5. Equations of first order and first degree (Exact equations). Supplemetary problems. Page 33
Problem number : 25 (d)
Date solved : Tuesday, September 30, 2025 at 05:09:58 PM
CAS classification : [[_homogeneous, `class D`], _rational, _Riccati]

\begin{align*} -y-3 x^{2} \left (x^{2}+y^{2}\right )+x y^{\prime }&=0 \end{align*}

✓ Maple. Time used: 0.004 (sec). Leaf size: 14

ode:=-y(x)-3*x^2*(x^2+y(x)^2)+x*diff(y(x),x) = 0; 
dsolve(ode,y(x), singsol=all);
 

\[ y = \tan \left (x^{3}+3 c_1 \right ) x \]

✓ Mathematica. Time used: 0.049 (sec). Leaf size: 30

ode=(-y[x]-3*x^2*(x^2+y[x]^2))+x*D[y[x],x]==0; 
ic={}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ \text {Solve}\left [\int _1^{\frac {y(x)}{x}}\frac {1}{K[1]^2+1}dK[1]=x^3+c_1,y(x)\right ] \]

✓ Sympy. Time used: 0.188 (sec). Leaf size: 27

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(-3*x**2*(x**2 + y(x)**2) + x*Derivative(y(x), x) - y(x),0) 
ics = {} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = \frac {x \left (i C_{1} + i e^{2 i x^{3}}\right )}{C_{1} - e^{2 i x^{3}}} \]