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Exercise

$\frac{dy}{dx}=\frac{y}{2xlnx}$

Step-by-step Solution

Learn how to solve separable differential equations problems step by step online. Solve the differential equation dy/dx=y/(2xln(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 \frac{1}{2x\ln\left(x\right)}dx. Integrate both sides of the differential equation, the left side with respect to y, and the right side with respect to x. Solve the integral \int\frac{1}{y}dy and replace the result in the differential equation.
Solve the differential equation dy/dx=y/(2xln(x))

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Final answer to the exercise

$y=C_1\sqrt{\ln\left(x\right)}$

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

$\frac{dy}{dx}=\frac{1}{6x-42}$

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

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

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

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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