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Exercise

$\frac{1}{3}\left(\frac{dy}{dx}-x\right)=x$

Step-by-step Solution

Learn how to solve separable differential equations problems step by step online. Solve the differential equation 1/3(dy/dx-x)=x. Multiply both sides of the equation by 3. We need to isolate the dependent variable y, we can do that by simultaneously subtracting -x from both sides of the equation. Combining like terms 3x and x. 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 1/3(dy/dx-x)=x

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Final answer to the exercise

$y=2x^2+C_0$

Try other ways to solve this exercise

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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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Similar Questions Solved

$\frac{dy}{dx}=y^2-9$

$\frac{dy}{dx}=y^2-4$

$\frac{dy}{dx}=y-y^2$

$\frac{dy}{dx}=y\left(y+2\right)$

$\frac{dy}{dx}=\left(1+e^{-x}\right)\left(y^2-1\right)$

$\frac{dy}{dx}=\frac{x}{2x-y}$

$\frac{dy}{dx}=y\left(1-y\right)$

Main Topic: Separable Differential Equations

A separable differential equation is one that can be solved by separating variables, that is, when all expressions involving a variable can be placed on one side of the equation, and expressions involving the other variable on the other side of the equation.

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