Final answer to the problem
$y=-\arctan\left(x+C_0\right)+x+1$
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Step-by-step Solution
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- 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
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1
Rewrite the differential equation using Leibniz notation
$\frac{dy}{dx}=\sin\left(x-y+1\right)^2$
Learn how to solve problems step by step online.
$\frac{dy}{dx}=\sin\left(x-y+1\right)^2$
Learn how to solve problems step by step online. Solve the differential equation y^'=sin(x-y+1)^2. 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
$y=-\arctan\left(x+C_0\right)+x+1$
