Final answer to the problem
$\ln\left|y\right|-\frac{1}{2}\ln\left|y^2+1\right|=\ln\left|x\right|+C_0$
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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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1
Rewrite the differential equation using Leibniz notation
$x\frac{dy}{dx}-y=y^3$
Learn how to solve problems step by step online.
$x\frac{dy}{dx}-y=y^3$
Learn how to solve problems step by step online. Solve the differential equation xy^'-y=y^3. Rewrite the differential equation using Leibniz notation. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -y from both sides of the equation. Multiply -1 times -1. Group the terms of the differential equation. Move the terms of the y variable to the left side, and the terms of the x variable to the right side of the equality.
Final answer to the problem
$\ln\left|y\right|-\frac{1}{2}\ln\left|y^2+1\right|=\ln\left|x\right|+C_0$
