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Exercise

(4y+x2y)dy=(2x+y2x)dx\left(4y+x^2y\right)dy=\left(2x+y^2x\right)dx

Step-by-step Solution

Learn how to solve problems step by step online. Solve the differential equation (4y+x^2y)dy=(2x+y^2x)dx. Divide both sides of the equation by dx. Factor the polynomial 2x+y^2x by it's greatest common factor (GCF): x. Factoring by y. 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 (4y+x^2y)dy=(2x+y^2x)dx

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Final answer to the exercise

ln⁡∣22+y2∣=ln⁡∣24+x2∣+C0\ln\left|\frac{\sqrt{2}}{\sqrt{2+y^2}}\right|=\ln\left|\frac{2}{\sqrt{4+x^2}}\right|+C_0

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  • Exact Differential Equation
  • Linear Differential Equation
  • Separable Differential Equations
  • 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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(4y+x2y)dy=(2x+y2x)dx
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