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