13.4.1 problem 3

Internal problem ID [2338]
Book : Differential equations and their applications, 3rd ed., M. Braun
Section : Section 1.9. Page 66
Problem number : 3
Date solved : Monday, January 27, 2025 at 05:47:56 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: 0.024 (sec). Leaf size: 19

dsolve(2*t*sin(y(t))+exp(t)*y(t)^3+(t^2*cos(y(t))+3*exp(t)*y(t)^2)*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: 0.408 (sec). Leaf size: 22

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

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