Determine an appropriate substitution and then solve the differential equation. ху'%3D у In(ху)

Q: Find a system of ordinary differential equations by the method of separation of variables. af af дх…

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Q: Solve the given differential equation by undetermined coefficients. у" - у' + = 5 + eX/2 y(x):

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Q: (4x'у — 15х? — у )ӑx +x* +3у? - х)dy-0

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Q: 3.- Show the differential equation is exact, then solve the equation. dy _ 3x2 - 6ху Зx? — у dx

A: To show that the differential equation is exact and to find the general solution

Q: y"-7y'=(2x-1)sin 2x

A: Differential equation

Q: 2x³y' = y(y² + 3x?)

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Q: Form the differential equation for the function xy = ae2x – be-2x a. xy" – y' = - 4xy O b. xy" – 2y'…

A: The given equation is xy=ae2x-be-2x. Evaluate the differential equation as follows.…

Q: A shrimp farm in thailand starts with 3,000 shrimp. the natural growth rate of shrimp is 12% per…

A: Given that a shrimp farm in Thailand starts with 3,000 shrimp that is at t=0 we have yt=3000 where…

Q: Write a differential equation that expresses the law ofnatural growth. What does it say in terms of…

A: To write: Differential equation that express the law of natural growth. And what does it say in…

Q: Solve the differential equation. (Assume the independent variable is x.) у" - у' — 20у 3о

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Q: One solution of the differential equation is given. Find the general solution. 5x у3) + Зу" - 15у'-…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.