14.3.7 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 : Monday, January 27, 2025 at 05:57:37 AM
CAS classification : [_exact, _rational, [_1st_order, `_with_symmetry_[F(x),G(x)]`], [_Abel, `2nd type`, `class A`]]

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

With initial conditions

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

✓ Solution by Maple

Time used: 0.018 (sec). Leaf size: 22

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

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

✓ Solution by Mathematica

Time used: 0.165 (sec). Leaf size: 25

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

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