Internal problem ID [14419]
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.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_exact]
\[ \boxed {t^{2} y+\left (\frac {t^{3}}{3}-\cos \left (y\right )\right ) y^{\prime }=-\sin \left (t \right )} \]
✓ Solution by Maple
Time used: 0.0 (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)
\[ \frac {t^{3} y \left (t \right )}{3}-\cos \left (t \right )-\sin \left (y \left (t \right )\right )+c_{1} = 0 \]
✓ Solution by Mathematica
Time used: 0.204 (sec). Leaf size: 22
DSolve[(t^2*y[t]+Sin[t])+(1/3*t^3-Cos[y[t]])*y'[t]==0,y[t],t,IncludeSingularSolutions -> True]
\[ \text {Solve}\left [t^3 y(t)-3 \sin (y(t))-3 \cos (t)=c_1,y(t)\right ] \]