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

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asin
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##  Final answer to the problem

$y=-2\arctan\left(\frac{x+C_1}{x+C_0}\right)+x+1$
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##  Step-by-step Solution 

How should I solve this problem?

• Choose an option
• Exact Differential Equation
• Linear Differential Equation
• Separable Differential Equation
• Homogeneous Differential Equation
• Integrate by partial fractions
• Product of Binomials with Common Term
• FOIL Method
• Integrate by substitution
• Integrate by parts
Can't find a method? Tell us so we can add it.
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Rewrite the differential equation using Leibniz notation

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

Learn how to solve differential equations problems step by step online.

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

Learn how to solve differential equations problems step by step online. Solve the differential equation y^'=sin(x-y+1). Rewrite the differential equation using Leibniz notation. When we identify that a differential equation has an expression of the form Ax+By+C, we can apply a linear substitution in order to simplify it to a separable equation. We can identify that x-y+1 has the form Ax+By+C. Let's define a new variable u and set it equal to the expression. Isolate the dependent variable y. Differentiate both sides of the equation with respect to the independent variable x.

##  Final answer to the problem

$y=-2\arctan\left(\frac{x+C_1}{x+C_0}\right)+x+1$

##  Explore different ways to solve this problem

Solving a math problem using different methods is important because it enhances understanding, encourages critical thinking, allows for multiple solutions, and develops problem-solving strategies. Read more

SnapXam A2

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2
3
4
5
6
7
8
9
0
a
b
c
d
f
g
m
n
u
v
w
x
y
z
.
(◻)
+
-
×
◻/◻
/
÷
2

e
π
ln
log
log
lim
d/dx
Dx
|◻|
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

###  Main Topic: Differential Equations

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