(a) Verify the solutions: (b) Verify y' = y y = e (linear equation) y' = -y²y = x (x 0) (nonlinear equation) y' = y y = ce y' = y²y = cx-¹ for all c for only c= 0,-1

Q: dy 4. x - y = x² sin x dx

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Q: Use the 2 solutions Bernoulli's equation y' + -√√y=0 y x

A: The given differential equation y'+yx-y=0. We have to find the solution of the differential…

Q: (x-2)(dy/dx) – y =(x-2)3 solve homogenous equation by linear equation method

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Q: show that y=x2 is one of this equation solutions x2y''-2y=0

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Q: x' = (C )x ´sec X + 0, 1

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Q: Given the Bernoulli's equation Dy/DX+yP(x)=y^n Q(x) and x=y^1-n, reduce the equation to the linear…

A: Given differential equation is                                           dydx+yP(x)=ynQ(x);  x=y1-n…

Q: Solve: y(4) + 18y"+81y = 0 y(0) = -4, y'(0) = 11, y"(0) = 60, y"(0) = -81

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Q: A state's licese plate has 7 characters. Each character can be a capital letter (A – Z), or a…

A: Number of license plates= (no .of arrangements of 3 capital letters )*(no. of arrangements of 4…

Q: y' = (x - 1)(y-2), y(2) = 4

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Q: What physical systems might the Chini equation, y*y' + f(x) = g(x)*y, represent? Can you tell me…

A: The Chini equation, given by  y∗y′+f(x)=g(x)∗y , appears in various physical and engineering…

Q: Height and Distance If an object is projected from the ground and lands on the ground some distance…

A: An equation of the trajectory y=ax2+bxWhere a<0 , b>0.The height is the maximum value of…

Q: x(y')2 - 2(y')3 - 2x - y = 0 find the general solution of the equation

A: Given differential equation is, xy'2-2y'3-2x-y=0 Let, the given equation be, y'=dydx=p Thus,…

Q: Solve y' = 12xy 2х, у(0) — 15 -

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Q: 3 (x-2) y'= y + 2(x-2)

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Q: Differentiate. Y(u) = (u-2 + u-3)(u5 - 6u²) Y'(u) = %3D

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Q: (x+1)3 solve for y'. %3D x2

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Q: Find y' y = 3x-2 2x+3

A: Given Functiony=(i) (ii) (iii)

Q: 2. (x2) y = y+2(x2)

A: Topic = Differential equation

Q: y'+(2x-1)y-xy2=x-1; y(0)=3, explicit solution of the form y=f(x) Also: a) Determine the value of…

A: A differential equation is a mathematical equation that connects one or more unknown functions with…

Q: y(4)+3y'''+2y''=12x2 High nonhomogeneous equations

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Q: Solve the first-order linear equation ey' + 3ey = 2xe¯ = 2xe-5x, y(1)= 232.

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Q: Use the particular solution method to solve y - y = 2e²

A: Given that  a first order linear differential equations and we find particular solution of this…

Q: Solve: y""-12y"+45y'-50y = 0 y(0) = −3, y'(0) = −11, y'(0) = -53 y(t) =

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Q: Solve: y""-9y" +24y+34y = 0 y(0) = 4, y'(0) = -1, y'(0) = -56 y(t) =

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