73.3.43 problem 4.8 (b)

Internal problem ID [15077]
Book : Ordinary Differential Equations. An introduction to the fundamentals. Kenneth B. Howell. second edition. CRC Press. FL, USA. 2020
Section : Chapter 4. SEPARABLE FIRST ORDER EQUATIONS. Additional exercises. page 90
Problem number : 4.8 (b)
Date solved : Tuesday, January 28, 2025 at 07:29:52 AM
CAS classification : [_separable]

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

With initial conditions

\begin{align*} y \left (0\right )&=-4 \end{align*}

✓ Solution by Maple

Time used: 0.236 (sec). Leaf size: 14

dsolve([y(x)*diff(y(x),x)=sin(x),y(0) = -4],y(x), singsol=all)
 

\[ y = -\sqrt {18-2 \cos \left (x \right )} \]

✓ Solution by Mathematica

Time used: 0.098 (sec). Leaf size: 28

DSolve[{y[x]*D[y[x],x]==Sin[x],{y[0]==-4}},y[x],x,IncludeSingularSolutions -> True]
 

\[ y(x)\to -\sqrt {2} \sqrt {\int _0^x\sin (K[1])dK[1]+8} \]