Internal problem ID [13021]
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).
ODE order: 1.
ODE degree: 1.
CAS Maple gives this as type [_separable]
\[ \boxed {y y^{\prime }=\sin \left (x \right )} \] With initial conditions \begin {align*} [y \left (0\right ) = -4] \end {align*}
✓ Solution by Maple
Time used: 0.14 (sec). Leaf size: 14
dsolve([y(x)*diff(y(x),x)=sin(x),y(0) = -4],y(x), singsol=all)
\[ y = -\sqrt {-2 \cos \left (x \right )+18} \]
✓ Solution by Mathematica
Time used: 0.11 (sec). Leaf size: 22
DSolve[{y[x]*y'[x]==Sin[x],{y[0]==-4}},y[x],x,IncludeSingularSolutions -> True]
\[ y(x)\to -\sqrt {2} \sqrt {9-\cos (x)} \]