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

Used Formulas

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Solution

Formulas

Videos

Special Products

· Perfect Square Trinomial
$a^2+2ab+b^2=(a+b)^2$
· Perfect Square Trinomial
$ a^2-2ab+b^2= (a-b)^2$

Integration Techniques

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

Basic Integrals

· Constant factor Rule
$\int cxdx=c\int xdx$
· Power Rule of Integration
$\int x^ndx=\frac{x^{\left(n+1\right)}}{n+1}+C$
· Integral of a Constant
$\int cdx=cvar+C$

Function Plot

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

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0
a
b
c
d
f
g
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

How to improve your answer:

Similar Problems Solved

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

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

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

$\frac{dy}{dx}=2-2sin\left(y\right)$

$\frac{dy}{dx}=4sin\left(20x-5y\right)$

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

$\frac{dy}{dx}=\cos\left(3x-y\right)$

Main Topic: Integrals of Rational Functions of Sine and Cosine

The integrals of rational functions of sine and cosine are integrals where the integrand is a rational function composed of sines and cosines, usually in the denominator, which is not easily reducible. However, these integrals are easy to solve by applying the recommended substitution: $z=\tan\left(\frac{x}{2}\right)$

Used Formulas

See formulas (5)

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