In Problems 35-40 solve the given differential equation by means of the substitution x = e'. d²y dy + 8y = x2 + 10x dx 35. x2 %3D dx?

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A: topic - differential equation

Q: 4. Find the general solution to the differential equation y²y" = y/ (where y' = )

A: To find solution of the differential equation: y2y''=y'

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A:

Q: Find the general solution for the differential equation y" + 2V3y" + 3y' = 7t2. %3D

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Q: 5. Show that if u is any solution to the differential equation y" = -y then u² + (u')² is a…

A: See below the solution

Q: 9. Find the general solution of the differential equation y" - 2y' = sin 4x.

A:

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Q: 1. Determine by direct substitution whether or not the equation y =| x²-2x et +2x+2 is a solution to…

A: Step 1:Step 2: Step 3: Step 4:

Q: 2. A patient is taking a medicine that has a half-life of 6 hours in the human body, meaning that…

A:

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.