Final answer to the problem
$y=\sqrt{2\left(\frac{\ln\left(\frac{x}{x-4}\right)}{4}+C_0\right)},\:y=-\sqrt{2\left(\frac{\ln\left(\frac{x}{x-4}\right)}{4}+C_0\right)}$
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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
Multiplying polynomials $dy$ and $x^2-4x$
$\frac{dx}{y}+x^2dy-4xdy=0$
Learn how to solve integrals by partial fraction expansion problems step by step online.
$\frac{dx}{y}+x^2dy-4xdy=0$
Learn how to solve integrals by partial fraction expansion problems step by step online. Solve the differential equation dx/y+(x^2-4x)dy=0. Multiplying polynomials dy and x^2-4x. Group the terms of the equation. Factor the polynomial x^2dy-4xdy by it's greatest common factor (GCF): xdy. 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
$y=\sqrt{2\left(\frac{\ln\left(\frac{x}{x-4}\right)}{4}+C_0\right)},\:y=-\sqrt{2\left(\frac{\ln\left(\frac{x}{x-4}\right)}{4}+C_0\right)}$
