Final answer to the problem
$\frac{-\ln\left|\sqrt{2}y+1\right|+\ln\left|\sqrt{2}y-1\right|}{6\sqrt{2}}=x+C_0$
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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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$\frac{dy}{dx}=6y^2-3$
Learn how to solve problems step by step online. Solve the differential equation y^'=6y^2-3. Rewrite the differential equation using Leibniz notation. 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. Simplify the expression \frac{1}{6y^2-3}dy. 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
$\frac{-\ln\left|\sqrt{2}y+1\right|+\ln\left|\sqrt{2}y-1\right|}{6\sqrt{2}}=x+C_0$
