Final answer to the problem
Step-by-step Solution
How should I solve this problem?
- 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
- Integrate using tabular integration
- Load more...
Rewrite the differential equation using Leibniz notation
Learn how to solve integrals of polynomial functions problems step by step online.
$x\frac{dy}{dx}+y\ln\left(x\right)=y\ln\left(y\right)+y$
Learn how to solve integrals of polynomial functions problems step by step online. Solve the differential equation xy^'+yln(x)=yln(y)+y. Rewrite the differential equation using Leibniz notation. We need to isolate the dependent variable y, we can do that by simultaneously subtracting y\ln\left(x\right) from both sides of the equation. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{y\ln\left(y\right)+y-y\ln\left(x\right)}{x} is homogeneous, since it is written in the standard form \frac{dy}{dx}=\frac{M(x,y)}{N(x,y)}, where M(x,y) and N(x,y) are the partial derivatives of a two-variable function f(x,y) and both are homogeneous functions of the same degree.