CM The initial value problem: x dy 2a²y = 23 .3 In(3) is linear. Find the explicit solution to this IVP. dx 1+ x³' Y(2) =1+"

Q: 1.

A: ∫-11∫-1-x20x2+y2dydxConvert to polar coordinates:=∫π2π∫01r2rdrdθ=∫π2π13dθ=π3

Q: ind the derivative with respect to x for the follo a. y = 43x b. f(x) = 22x3cos x c. y = tan(23*) d.…

A: Since you have posted multiple questions with multiple subparts, we will solve the first three…

Q: -3 2. S x*Vx Vx²-9

A: Integration is the process of finding the anti-derivative function of the given function. The…

Q: dP Pt, P(1) = 3 %3D dt

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Q: Compute if df = 2 and dx du dx = 6.

A: It is given that,

Q: [  (1+ xsiny)dx - x2cosydy = 0  ] How can I find the solution "y" of this equation?

A: We shall use basic knowledge of first order ordinary differential equations to solve this question.…

Q: Se-¹x² dx. е

A: Given query is to find the integral.

Q: Differentiate. y = In |4x² - 7x|

A: solution:-y=ln4x2-7xdydx=ddxln4x2-7x       =14x2-7xddx4x2-7x      {chain rule}      =8x-74x2-7x

Q: Find dy/dx. y = __2x + 3)3__ (4x 2 − 1)8

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Q: If x2+y2-2axy=1  then find (dy/dx)

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Q: Find dy/dx.

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Given x = (3x + 4y) Find dy/ dx with explanation hopefully

A: Given: x=3x+4y To Find: dydx=?

Q: Solve the Linear DE: 2y (y2 - x) dy = dx. %3D

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Q: Find the values of d/dx (11) and d/dx(π)

A: Consider the provided information, ddx11   and   ddxπ. Find the values of the derivative. The…

Q: I. Find dy/dx of the following: 1. y= In 2x 2. y= (In.x) 3. y = In(tan.x)

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Q: 3 7x + 6x - 5x dy find dx - Example 28. If y = 4

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Q: I241 Solve the DE. (3x²y- xy)dx+(2r'y² +x*y*)dy = 0.

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Q: 2. Evaluate the following: . /32 dx a. b. /a'e'dt c. [e*se" dx

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Q: Solve the following DE • X – dy =2

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Describe two ways to find the general solution of (dy/dx) + 3xy = x. Verify that each method gives…

A: Given: The differential equation is dydx+3xy=x We have to find the general solution by two ways.

Q: (e 2X Integrate 2X to dx

A: The given integral is ∫e2x+1xe2x-1xdx   Formula used: a2-b2=a+ba-b

Q: d 4. Simplify. dx (t² + 1) dt 2x

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Q: 0.1. Solve the following equations by using undetermined method: d*y d'y +16 y =0 +8- dx dx?

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Q: (e* + 1)ydy = (y + 1)e*dx

A: Given differential equation is (ex+1)ydy=(y+1)exdx⇒ydyy+1=exex+1dx⇒1-1y+1dy=exex+1dx

Q: Use Euler's method to numerically integrate dy -2x3 + 12x2 – 20x + 8.5 %3D dx from x = 0 to x = 0.5…

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Q: [ a(x+y) - xty]dy = (x+xy²- 2y +3)d« when x-1, yal 3. %3D (9xy - 2y²) dx - ( 6x²_ xy) dy =0 4.

A: I have authority to answer one question only, if you want another question to be solved then upload…

Q: x'+ x°)dx (x³+5) to 3

A: Given ∫x5+x2(x3+5)10dx

Q: Solve the homogenous DE Solve: xy dx - (x + 2y)^2 dy = 0.

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Q: Solve the following IVP: dy sin(z*)e %3D dx y(2) = V5 %3D

A: Use separation of variables method on dydx=sinx2ex3 dy=sinx2ex3dx Now integrate both sides without…

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.