74.4.44 problem 44

Internal problem ID [15937]
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 : 44
Date solved : Tuesday, January 28, 2025 at 08:23:34 AM
CAS classification : [_quadrature]

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

With initial conditions

\begin{align*} x \left (0\right )&=0 \end{align*}

✓ Solution by Maple

Time used: 0.016 (sec). Leaf size: 14

dsolve([sin(y)^2=diff(x(y),y),x(0) = 0],x(y), singsol=all)
 

\[ x \left (y \right ) = \frac {y}{2}-\frac {\sin \left (2 y \right )}{4} \]

✓ Solution by Mathematica

Time used: 0.013 (sec). Leaf size: 17

DSolve[{Sin[y]^2==D[x[y],y],{x[0]==0}},x[y],y,IncludeSingularSolutions -> True]
 

\[ x(y)\to \int _0^y\sin ^2(K[1])dK[1] \]