(2x+1) (xo1) y" +2xy'- 2y =(2x+1)* %3D * Find the second solution if a solution off the homogeneous form of given differential equation is y = (x+1) -" * Show that the solutions dre linear independent. , Find the general solution of the inhomogeneous equation.

Q: Pregunta 13 The price p (in dollars) and the demand x for a brand of running shoes are related by…

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Q: he slope of the line tangent to the curve y = x -8x3 + 22x2 - 24x +9 at x=1 is (a) -2 (b) 2 (c) 0…

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Q: 14. (x+ y) dx + (x + 2y) dy = 0, y(2) = 3 %3D

A: To solve the first order differential equation we first arranging the term in such a way that after…

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Q: Write the slope-intercept form of the equation of the line passing through (0,-12) and (6,6). O y =…

A: Write the slope intercept form of the equation of the line passing through (0,-12) and (6,6)

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Q: Linear equation of Order one 1. (x* + 2y)dx – xdy = 0 2. y' = csc x – y cot x

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A: Given:  Aim:  Basic information:  Using central difference metthodf'xn = fxn+1-fxn-12xn-xn-1

Q: y" + 2y - 15y = 5t²e³t with y(0) = 6, y(0) = -6

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Q: = x³ +. 5. f(x) = 忘 3x = y + 4 = U x + 2y 6=0

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Q: i) Find an equation of the line tangent to f(x) = 2x - at (0₁-12). 2

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Q: . Let f: R²R where f(x, y) = √√√1-x² - y² and c = (0, -2). (a) Find and simplify Df(c). (b) Find and…

A: (a) Given fx,y=1-x2-y2, c=0,-22 ∂f∂x=-2x21-x2-y2∂f∂x0,-22=0∂f∂y=-2y21-x2-y2∂f∂y0,-22=221-0-12=1…

Q: What is the equation of the curve that passes y? slope of at any point (x, y)? Væ+3

A: Given, slope of the curve at any point (x, y) is  y2x+3.

Q: higher order derivatives x + xy + y = 1 , find y′′

A: The question is about Implicit differentiation. In implicit differentiation, we do not separate the…

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Q: x= y2-5 x-intercept     (x, y) = y-intercept (x,y)=          (smaller y-value) y-intercept (x,y)=…

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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.