Final answer to the problem
$p=w+\sqrt{-2w+C_1},\:p=w-\sqrt{-2w+C_1}$
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Step-by-step Solution
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- Exact Differential Equation
- Linear Differential Equation
- Separable Differential Equation
- 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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1
Group the terms of the equation
Learn how to solve integrals of polynomial functions problems step by step online.
$\left(p-w\right)dp=-dw$
Learn how to solve integrals of polynomial functions 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.
Final answer to the problem
$p=w+\sqrt{-2w+C_1},\:p=w-\sqrt{-2w+C_1}$
