14.3.1 problem 3

Internal problem ID [2510]
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 : 3
Date solved : Monday, January 27, 2025 at 05:56:34 AM
CAS classification : [_exact]

\begin{align*} 2 t \sin \left (y\right )+{\mathrm e}^{t} y^{3}+\left (t^{2} \cos \left (y\right )+3 \,{\mathrm e}^{t} y^{2}\right ) y^{\prime }&=0 \end{align*}

✓ Solution by Maple

Time used: 0.025 (sec). Leaf size: 19

dsolve((2*t*sin(y(t))+y(t)^3*exp(t))+(t^2*cos(y(t))+3*y(t)^2*exp(t))*diff(y(t),t)=0,y(t), singsol=all)
 

\[ {\mathrm e}^{t} y^{3}+\sin \left (y\right ) t^{2}+c_1 = 0 \]

✓ Solution by Mathematica

Time used: 0.447 (sec). Leaf size: 22

DSolve[(2*t*Sin[y[t]]+y[t]^3*Exp[t])+(t^2*Cos[y[t]]+3*y[t]^2*Exp[t])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [t^2 \sin (y(t))+e^t y(t)^3=c_1,y(t)\right ] \]