Mathematics, 08.10.2020 18:01 jess2828
Show that an implicit solution of 2x sin2(y) dx - (x2 + 11) cos(y) dy = 0 is given by ln(x2 + 11) + csc(y) = C.
Differentiating ln(x2 + 11) + csc(y) = C we get 2x/ x2 + 11 (__) dy/dy=0 or
2x sin2(y) dx + ()dy = 0.
Find the constant solutions, if any, that were lost in the solution of the differential equation. (Let k represent an arbitrary integer.)
y =
Answers: 1
![0 = \frac{2x}{ x^2 + 11} + [-cot * csc(y) ]\frac{dy}{dx}](/tpl/images/0794/3994/af403.png)
![0 = \frac{2x}{ x^2 + 11} + [-\frac{cos(y)}{ sin(y) }* \frac{1}{sin(y)} ]\frac{dy}{dx}](/tpl/images/0794/3994/d673c.png)
![0 = \frac{2x}{ x^2 + 11} + [-\frac{cos(y)}{ sin^2(y) }]\frac{dy}{dx}](/tpl/images/0794/3994/bcec5.png)
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![2 x (sin^2(y) dx + [-cos(y) (x^2 + 11)]dy = 0](/tpl/images/0794/3994/9e420.png)
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Show that an implicit solution of 2x sin2(y) dx - (x2 + 11) cos(y) dy = 0 is given by ln(x2 + 11) +...
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