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Exercise

$\left(p-w\right)\:dp\:+\:dw\:=\:0$

Step-by-step Solution

Learn how to solve problems step by step online. Solve the differential equation (p-w)dp+dw=0. Group the terms of the equation. Divide both sides of the equation by dw. Rewrite the differential equation. When we identify that a differential equation has an expression of the form Ax+By+C, we can apply a linear substitution in order to simplify it to a separable equation. We can identify that p-w has the form Ax+By+C. Let's define a new variable u and set it equal to the expression.
Solve the differential equation (p-w)dp+dw=0

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Final answer to the exercise

$p=w+\sqrt{-2w+C_1},\:p=w-\sqrt{-2w+C_1}$

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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