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Exercise

$\left(xy^2-x\right)dx+\left(y-x^2y\right)dy=0$

Step-by-step Solution

Learn how to solve problems step by step online. Solve the differential equation (xy^2-x)dx+(y-x^2y)dy=0. Factoring by x. Factoring by y. Grouping the terms of the differential equation. 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.
Solve the differential equation (xy^2-x)dx+(y-x^2y)dy=0

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Final answer to the exercise

$y=\sqrt{C_4+C_3x^2},\:y=-\sqrt{C_5+C_3x^2}$

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  • Homogeneous Differential Equation
  • Integrate by partial fractions
  • Product of Binomials with Common Term
  • FOIL Method
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