Mister Exam

# Differential equation tgy*y'=ctgx

y() =
y'() =
y''() =
y'''() =
y''''() =

from to

### The solution

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d
--(y(x))*tan(y(x)) = cot(x)
dx                         
$$\tan{\left(y{\left(x \right)} \right)} \frac{d}{d x} y{\left(x \right)} = \cot{\left(x \right)}$$
tan(y)*y' = cot(x)
             /  C1  \
y(x) = - acos|------| + 2*pi
\sin(x)/       
$$y{\left(x \right)} = - \operatorname{acos}{\left(\frac{C_{1}}{\sin{\left(x \right)}} \right)} + 2 \pi$$
           /  C1  \
y(x) = acos|------|
\sin(x)/
$$y{\left(x \right)} = \operatorname{acos}{\left(\frac{C_{1}}{\sin{\left(x \right)}} \right)}$$
Graph of the Cauchy problem
The classification
separable
1st exact
lie group
separable Integral
1st exact Integral
(x, y):
(-10.0, 0.75)
(-7.777777777777778, -9.53318197297792e-10)
(-5.555555555555555, 2.17e-322)
(-3.333333333333333, nan)
(-1.1111111111111107, 2.78363573e-315)
(1.1111111111111107, 6.971028255580836e+173)
(3.333333333333334, 3.1933833808213398e-248)
(5.555555555555557, 1.8642114079304264e+160)
(7.777777777777779, 8.38824356735529e+296)
(10.0, 1.202657649977811e-153)
(10.0, 1.202657649977811e-153)
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