Internal problem ID [13299]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y^{\prime }-3 y^{2}+\sin \left (x \right ) y^{2}=0} \]
✓ Solution by Maple
Time used: 0.0 (sec). Leaf size: 17
dsolve(diff(y(x),x)=3*y(x)^2-y(x)^2*sin(x),y(x), singsol=all)
\[ y \left (x \right ) = -\frac {1}{\cos \left (x \right )-c_{1} +3 x} \]
✓ Solution by Mathematica
Time used: 0.156 (sec). Leaf size: 22
DSolve[y'[x]==3*y[x]^2-y[x]^2*Sin[x],y[x],x,IncludeSingularSolutions -> True]
\begin{align*} y(x)\to -\frac {1}{3 x+\cos (x)+c_1} \\ y(x)\to 0 \\ \end{align*}