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Solve the differential equation $y^{\prime}\cos\left(x\right)+y\sin\left(x\right)=1$

Used Formulas

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Solution

Formulas

Videos

Integration Techniques

· Integration by Substitution
$\int f\left(x\right)dx=\int f\left(g\left(t\right)\right) g'\left(t\right)dt$

Special Products

· Square of a difference
$\left(a+b\right)^2=a^2+2ab+b^2$
· Perfect Square Trinomial
$a^2+2ab+b^2=(a+b)^2$
· Perfect Square Trinomial
$ a^2-2ab+b^2= (a-b)^2$
· Difference of two Squares
$a^2-b^2=(a+b)(a-b)$

Basic Integrals

· Sum Rule for Integration
$\int\left(a+b+...\right)dx=\int adx+\int bdx+...$
· Constant factor Rule
$\int cxdx=c\int xdx$

Integrals of Rational Functions

$\int\frac{n}{x+b}dx=nsign\left(x\right)\ln\left(x+b\right)+C$

Trigonometric Identities

$\cos\left(\theta \right)^2=1-\sin\left(\theta \right)^2$

Trigonometric Integrals

$\int\csc\left(\theta \right)dx=-\ln\left(\csc\left(\theta \right)+\cot\left(\theta \right)\right)+C$
$\int\csc\left(\theta \right)^ndx=\frac{-\csc\left(\theta \right)^{\left(n-2\right)}\cot\left(\theta \right)}{n-1}+\frac{n-2}{n-1}\int\csc\left(\theta \right)^{\left(n-2\right)}dx$

Function Plot

Plotting: $y\cos\left(x\right)^{-1}=\ln\left(\frac{\tan\left(\frac{x}{2}\right)-1}{\tan\left(\frac{x}{2}\right)+1}\right)+\frac{-2\tan\left(\frac{x}{2}\right)}{\tan\left(\frac{x}{2}\right)^{2}-1}+2\ln\left(\frac{\tan\left(\frac{x}{2}\right)+1}{\sqrt{\tan\left(\frac{x}{2}\right)^{2}-1}}\right)+C_0$

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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:

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: Differential Equations

A differential equation is a mathematical equation that relates some function with its derivatives.

Used Formulas

See formulas (10)

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