consider-the-differential-equation-ytsinyyprimetsin-y-for-y2y-frac2-which-initia

Question

Consider the differential equation y′(t)=sin⁡$$yy^{\prime}(t$$)=\sin y for ∣y∣≤π2|y| ≤ \frac{π}{2}. Which initial conditions y(0)=By(0) = B lead to solutions that are increasing in time?

Accepted Answer

0B≤π20

Answer

0≤B≤π20\le B\le\frac{\pi}{2}

Answer

−π2≤B0-\frac{\pi}{2}\le B

Answer

−π2≤B≤0-\frac{\pi}{2}\le B\le0

Consider the differential equation y′(t)=sinyy^{\(\prime\)}(t)=\(\sin\) y for ∣y∣≤π2|y| ≤ \(\frac{π}{2}\). Which initial conditions y(0)=By(0) = B lead to solutions that are increasing in time?

Consider the differential equation $y^{'} (t) = \sin y$ for $∣ y ∣ \leq \frac{π}{2}$ . Which initial conditions $y of 0 equals B$ lead to solutions that are increasing in time?