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Exercise

$y'=2xy+exp\left(x^2\right)$

Step-by-step Solution

Learn how to solve separable differential equations problems step by step online. Solve the differential equation y^'=ex+px^2. Rewrite the differential equation using Leibniz notation. Factor the polynomial ex+px^2 by it's greatest common factor (GCF): 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. Simplify the expression x\left(e+px\right)dx.
Solve the differential equation y^'=ex+px^2

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Final answer to the exercise

$y=\frac{e}{2}x^2+\frac{x^{3}p}{3}+C_0$

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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