Question

(ODE) Doing some sample final exam problems to get me ready for my final in five and a half hours. Prompt posted below.

Answer 1

\[\frac{y}{\sqrt{4-x^2}}\frac{dy}{dx}=y^2+5\]\[\text{Solve the differential Equation.}\]

Answer 2

I think it's separable, so I'm going to treat it as such and take a shot at it like that.

Answer 3

\[\frac{1}{\sqrt{4-x^2}}\frac{dy}{dx}=\frac{y^2+5}{y}\]

Answer 4

\[\frac{y}{y^2+5}dy=\sqrt{4-x^2}\]

Answer 5

\[u=y^2+5, \ du=2ydy;\]\[\frac{1}{2}\int\limits_{}^{}\frac{1}{u}du=\int\limits_{}^{}\sqrt{4-x^2}dx\]

Answer 6

\[\frac{1}{2}\ln(y^2+5)=2\int\limits_{}^{}\cos^{2}(\theta)\]