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Solve the differential equation $y^{\prime}=\cos\left(x\right)\tan\left(y\right)$

Step-by-step Solution

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Solution

Formulas

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Final answer to the problem

$y=\arcsin\left(c_1e^{\sin\left(x\right)}\right)$
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Step-by-step Solution

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Learn how to solve separable differential equations problems step by step online. Solve the differential equation y^'=cos(x)tan(y). Rewrite the differential equation using Leibniz notation. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality. Simplify the expression \frac{1}{\tan\left(y\right)}dy. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.

Final answer to the problem

$y=\arcsin\left(c_1e^{\sin\left(x\right)}\right)$

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Function Plot

Plotting: $y=\arcsin\left(c_1e^{\sin\left(x\right)}\right)$

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0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
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×
◻/◻
/
÷
◻2
◻◻
√◻
√

◻√◻
◻√
∞
e
π
ln
log
log◻
lim
d/dx
D□x
∫
∫◻
|◻|
θ
=
>
<
>=
<=
sin
cos
tan
cot
sec
csc

asin
acos
atan
acot
asec
acsc

sinh
cosh
tanh
coth
sech
csch

asinh
acosh
atanh
acoth
asech
acsch

How to improve your answer:

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Main Topic: Separable Differential Equations

The easiest type of differential equations.

Used Formulas

See formulas (2)

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