73.3.1 problem 4.3 (a)

Internal problem ID [15035]
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 : 4.3 (a)
Date solved : Tuesday, January 28, 2025 at 07:28:09 AM
CAS classification : [_separable]

\begin{align*} y^{\prime }&=3 y^{2}-y^{2} \sin \left (x \right ) \end{align*}

✓ Solution by Maple

Time used: 0.002 (sec). Leaf size: 17

dsolve(diff(y(x),x)=3*y(x)^2-y(x)^2*sin(x),y(x), singsol=all)
 

\[ y = -\frac {1}{\cos \left (x \right )-c_{1} +3 x} \]

✓ Solution by Mathematica

Time used: 0.134 (sec). Leaf size: 31

DSolve[D[y[x],x]==3*y[x]^2-y[x]^2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
 

\begin{align*} y(x)\to -\frac {1}{\int _1^x(3-\sin (K[1]))dK[1]+c_1} \\ y(x)\to 0 \\ \end{align*}