8.3.7 problem 9

Internal problem ID [2516]
Book : Differential equations and their applications, 4th ed., M. Braun
Section : Chapter 1. First order differential equations. Section 1.9. Exact equations. Excercises page 66
Problem number : 9
Date solved : Tuesday, September 30, 2025 at 05:40:59 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

\begin{align*} 3 t^{2}+4 t y+\left (2 y+2 t^{2}\right ) y^{\prime }&=0 \end{align*}

With initial conditions

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

✓ Maple. Time used: 0.065 (sec). Leaf size: 22

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

\[ y = -t^{2}+\sqrt {t^{4}-t^{3}+1} \]

✓ Mathematica. Time used: 0.087 (sec). Leaf size: 25

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

\begin{align*} y(t)&\to \sqrt {t^4-t^3+1}-t^2 \end{align*}

✗ Sympy

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

Timed Out