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Exercise

$y'=\frac{y}{x}+5x$

Step-by-step Solution

Learn how to solve problems step by step online. Solve the differential equation y^'=y/x+5x. Rewrite the differential equation using Leibniz notation. Rearrange the differential equation. Simplifying. We can identify that the differential equation has the form: \frac{dy}{dx} + P(x)\cdot y(x) = Q(x), so we can classify it as a linear first order differential equation, where P(x)=\frac{-1}{x} and Q(x)=5x. In order to solve the differential equation, the first step is to find the integrating factor \mu(x).
Solve the differential equation y^'=y/x+5x

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Final answer to the exercise

$y=\left(5x+C_0\right)x$

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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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