74.4.50 problem 50

Internal problem ID [15943]
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
Date solved : Tuesday, January 28, 2025 at 08:24:06 AM
CAS classification : [_quadrature]

\begin{align*} y^{\prime }&=t \sin \left (t^{2}\right ) \end{align*}

With initial conditions

\begin{align*} y \left (\sqrt {\pi }\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.019 (sec). Leaf size: 12

dsolve([diff(y(t),t)=t*sin(t^2),y(Pi^(1/2)) = 0],y(t), singsol=all)
 

\[ y = -\frac {\cos \left (t^{2}\right )}{2}-\frac {1}{2} \]

✓ Solution by Mathematica

Time used: 0.021 (sec). Leaf size: 24

DSolve[{D[y[t],t]==t*Sin[t^2],{y[Sqrt[Pi]]==0}},y[t],t,IncludeSingularSolutions -> True]
 

\[ y(t)\to \int _{\sqrt {\pi }}^tK[1] \sin \left (K[1]^2\right )dK[1] \]