68.4.50 problem 50

Internal problem ID [17230]
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 : Thursday, October 02, 2025 at 01:59:13 PM
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*}

✓ Maple. Time used: 0.024 (sec). Leaf size: 12

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

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

✓ Mathematica. Time used: 0.013 (sec). Leaf size: 24

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

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

✓ Sympy. Time used: 0.107 (sec). Leaf size: 14

from sympy import * 
t = symbols("t") 
y = Function("y") 
ode = Eq(-t*sin(t**2) + Derivative(y(t), t),0) 
ics = {y(sqrt(pi)): 0} 
dsolve(ode,func=y(t),ics=ics)
 

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