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Exercise

$\frac{dy}{dx}=5x^4\left(4-y\right)dx$

Step-by-step Solution

Learn how to solve separable differential equations problems step by step online. Solve the differential equation dy/dx=5x^4(4-y)dx. Multiply both sides of the equation by dx. When multiplying two powers that have the same base (dx), you can add the exponents. Multiply 5 times 2. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x.
Solve the differential equation dy/dx=5x^4(4-y)dx

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Final answer to the exercise

$y=C_2e^{-2x^{5}}+4$

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

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

$ydy=4x\left(y^2+1\right)^{\frac{1}{2}}dx$

$\frac{dy}{dx}=\sin5x$

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

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

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

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

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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