** Final answer to the problem

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** Step-by-step Solution **

** How should I solve this problem?

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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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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 $\left(x+y+1\right)$ has the form $Ax+By+C$. Let's define a new variable $u$ and set it equal to the expression

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

$u=x+y+1$

Learn how to solve differential equations problems step by step online. Solve the differential equation dy/dx=(x+y+1)^2. 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 \left(x+y+1\right) 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. Now, substitute \left(x+y+1\right) and \frac{dy}{dx} on the original differential equation. We will see that it results in a separable equation that we can easily solve.

** Final answer to the problem

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