Internal problem ID [14208]
Book: INTRODUCTORY DIFFERENTIAL EQUATIONS. Martha L. Abell, James P. Braselton.
Fourth edition 2014. ElScAe. 2014
Section: Chapter 2. First Order Equations. Exercises 2.2, page 39
Problem number: 50.
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_quadrature]
\[ \boxed {y^{\prime }=t \sin \left (t^{2}\right )} \] With initial conditions \begin {align*} \left [y \left (\sqrt {\pi }\right ) = 0\right ] \end {align*}
✓ Solution by Maple
Time used: 0.016 (sec). Leaf size: 12
dsolve([diff(y(t),t)=t*sin(t^2),y(Pi^(1/2)) = 0],y(t), singsol=all)
\[ y \left (t \right ) = -\frac {\cos \left (t^{2}\right )}{2}-\frac {1}{2} \]
✓ Solution by Mathematica
Time used: 0.013 (sec). Leaf size: 17
DSolve[{y'[t]==t*Sin[t^2],{y[Sqrt[Pi]]==0}},y[t],t,IncludeSingularSolutions -> True]
\[ y(t)\to -\cos ^2\left (\frac {t^2}{2}\right ) \]