67.7.26 problem 26

Internal problem ID [16471]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 8. Review exercises for part of part II. page 143
Problem number : 26
Date solved : Thursday, October 02, 2025 at 01:34:44 PM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=x y^{2}+3 y^{2}+x +3 \end{align*}

✓ Maple. Time used: 0.003 (sec). Leaf size: 15

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

\[ y = \tan \left (\frac {1}{2} x^{2}+c_1 +3 x \right ) \]

✓ Mathematica. Time used: 0.147 (sec). Leaf size: 36

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

\begin{align*} y(x)&\to \text {InverseFunction}\left [\int _1^{\text {$\#$1}}\frac {1}{K[1]^2+1}dK[1]\&\right ]\left [\frac {x^2}{2}+3 x+c_1\right ] \end{align*}

✓ Sympy. Time used: 0.425 (sec). Leaf size: 14

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

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