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dydx=x2(x2+5x+6)\frac{dy}{dx}=x^2\left(x^2+5x+6\right)

Step-by-step Solution

Learn how to solve separable differential equations problems step by step online. Solve the differential equation dy/dx=x^2(x^2+5x+6). 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^2\left(x^2+5x+6\right)dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Expand the integral \int\left(x^{4}+5x^{3}+6x^2\right)dx into 3 integrals using the sum rule for integrals, to then solve each integral separately.
Solve the differential equation dy/dx=x^2(x^2+5x+6)

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Final answer to the exercise

y=x55+5x44+2x3+C0y=\frac{x^{5}}{5}+\frac{5x^{4}}{4}+2x^{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

dydx=y2−9\frac{dy}{dx}=y^2-9

dydx=y2−4\frac{dy}{dx}=y^2-4

dydx=y−y2\frac{dy}{dx}=y-y^2

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

dydx=(1+e−x)(y2−1)\frac{dy}{dx}=\left(1+e^{-x}\right)\left(y^2-1\right)

dydx=x2x−y\frac{dy}{dx}=\frac{x}{2x-y}

dydx=y(1−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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dydx =x2(x2+5x+6)
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