Final answer to the problem
$y=\sqrt{-\frac{1}{2}\ln\left(x+1\right)+\frac{1}{2}\ln\left(-x+1\right)+C_0},\:y=-\sqrt{-\frac{1}{2}\ln\left(x+1\right)+\frac{1}{2}\ln\left(-x+1\right)+C_0}$
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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
Group the terms of the equation
Learn how to solve integrals by partial fraction expansion problems step by step online.
$-2x^2y\cdot dy+2y\cdot dy=-dx$
Learn how to solve integrals by partial fraction expansion problems step by step online. Solve the differential equation dx-2x^2ydy2ydy=0. Group the terms of the equation. Factor the polynomial -2x^2y\cdot dy+2y\cdot dy by it's greatest common factor (GCF): 2y\cdot dy. 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. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Final answer to the problem
$y=\sqrt{-\frac{1}{2}\ln\left(x+1\right)+\frac{1}{2}\ln\left(-x+1\right)+C_0},\:y=-\sqrt{-\frac{1}{2}\ln\left(x+1\right)+\frac{1}{2}\ln\left(-x+1\right)+C_0}$
