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Solve the differential equation $\frac{dy}{dx}\cos\left(x\right)+y\sin\left(x\right)=1$

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Solution

Formulas

Videos

Proof the identity sin(x)^2 = 1 - cos(x)^2

https://www.youtube.com/watch?v=g7eVgtmQ7Dk

Homogeneous Differential Equations

https://www.youtube.com/watch?v=ZEJVyybsiT4

Algebra 2 - Solve a system of equation when they are the same line, 3x - 2y = -15; x - (2/3)y = -5

https://www.youtube.com/watch?v=nrrINRUnk74

Tutorial - How to solve a equation using difference of two angles, cos(x + (pi)/6)-cos(x - (pi)/6)=1

https://www.youtube.com/watch?v=f-HJVxlmuKM

Algebra 2 - Learn to solve a rational equation by multiplying by the LCD (15/x)+((9x-7)/(x+2))=9

https://www.youtube.com/watch?v=BMSmvkWcVTU

Algebra 2 - Solving a factored quadratic equation using the zero product property, -x(3x + 5) = 0

https://www.youtube.com/watch?v=3on6rsKoK_k

Function Plot

Plotting: $\frac{dy}{dx}\cos\left(x\right)+y\sin\left(x\right)-1$

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a
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d
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m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
◻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

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Similar Problems Solved

$\cos\left(x\right)\frac{dy}{dx}+\left(\sin\left(x\right)\right)y=1$

$cosx\frac{dy}{dx}+\left(senx\right)y=1$

$cosx\frac{dy}{dx}+ysenx=1$

$Cosx\frac{dy}{dx}+ySenx=1$

$\frac{dy}{dx}cosx+ysenx=1$

$\frac{dy}{dx}=\tan\left(x+y\right)$

Find the integral

$\int\frac{1}{\sin\left(x\right)-\cos\left(x\right)}dx$

Main Topic: Weierstrass Substitution

In integral calculus, the Weierstrass substitution or tangent half angle substitution is a method for solving integrals, which converts a rational expression of trigonometric functions into an algebraic rational function, which can be easier to integrate. The Weierstrass substitution is very useful for integrals that involve a simple rational expression with sine and/or cosine in the denominator.

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