47.1.13 problem 13

Internal problem ID [7394]
Book : Ordinary differential equations and calculus of variations. Makarets and Reshetnyak. Wold Scientific. Singapore. 1995
Section : Chapter 1. First order differential equations. Section 1.1 Separable equations problems. page 7
Problem number : 13
Date solved : Wednesday, March 05, 2025 at 04:25:19 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=\frac {3 x^{2}+4 x +2}{2 y-2} \end{align*}

With initial conditions

\begin{align*} y \left (0\right )&=-1 \end{align*}

✓ Maple. Time used: 0.460 (sec). Leaf size: 19

ode:=diff(y(x),x) = (3*x^2+4*x+2)/(-2+2*y(x)); 
ic:=y(0) = -1; 
dsolve([ode,ic],y(x), singsol=all);
 

\[ y = 1-\sqrt {\left (x +2\right ) \left (x^{2}+2\right )} \]

✓ Mathematica. Time used: 0.144 (sec). Leaf size: 26

ode=D[y[x],x]==(3*x^2+4*x+2)/(2*(y[x]-1)); 
ic={y[0]==-1}; 
DSolve[{ode,ic},y[x],x,IncludeSingularSolutions->True]
 

\[ y(x)\to 1-\sqrt {x^3+2 x^2+2 x+4} \]

✓ Sympy. Time used: 0.575 (sec). Leaf size: 20

from sympy import * 
x = symbols("x") 
y = Function("y") 
ode = Eq(Derivative(y(x), x) - (3*x**2 + 4*x + 2)/(2*y(x) - 2),0) 
ics = {y(0): -1} 
dsolve(ode,func=y(x),ics=ics)
 

\[ y{\left (x \right )} = 1 - \sqrt {x^{3} + 2 x^{2} + 2 x + 4} \]