74.8.17 problem 17

Internal problem ID [16153]
Book : INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton. Fourth edition 2014. ElScAe. 2014
Section : Chapter 2. First Order Equations. Review exercises, page 80
Problem number : 17
Date solved : Tuesday, January 28, 2025 at 08:52:51 AM
CAS classification : [_exact]

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

✓ Solution by Maple

Time used: 0.013 (sec). Leaf size: 21

dsolve((t^2*y(t)+sin(t))+(1/3*t^3-cos(y(t)))*diff(y(t),t)=0,y(t), singsol=all)
 

\[ \frac {y t^{3}}{3}-\cos \left (t \right )-\sin \left (y\right )+c_{1} = 0 \]

✓ Solution by Mathematica

Time used: 0.209 (sec). Leaf size: 60

DSolve[(t^2*y[t]+Sin[t])+(1/3*t^3-Cos[y[t]])*D[y[t],t]==0,y[t],t,IncludeSingularSolutions -> True]
 

\[ \text {Solve}\left [\int _1^{y(t)}\left (t^3-3 \cos (K[2])-\int _1^t3 K[1]^2dK[1]\right )dK[2]+\int _1^t\left (3 y(t) K[1]^2+3 \sin (K[1])\right )dK[1]=c_1,y(t)\right ] \]