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- Linear Differential Equation
- Exact 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
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We need to isolate the dependent variable $y$, we can do that by simultaneously subtracting $x^3-2y^3$ from both sides of the equation
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$3xy^2\left(\frac{dy}{dx}\right)=-\left(x^3-2y^3\right)$
Learn how to solve problems step by step online. Solve the differential equation x^3-2y^33xy^2dy/dx=0. We need to isolate the dependent variable y, we can do that by simultaneously subtracting x^3-2y^3 from both sides of the equation. Rewrite the differential equation. We can identify that the differential equation \frac{dy}{dx}=\frac{-\left(x^3-2y^3\right)}{3xy^2} 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. Use the substitution: y=ux.