Consider the differential equation (DE) y" +t(y')² = 0. a) Its i) order is ii) degree is b) Generally, when we have a DE of the same order as the one given above, how many conditions do we need in order to find a particular solution?

Q: A1. The differential equation of the function y = ax? + b where 'a' and 'b' are constant is: a) y' =…

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Q: Find the general solution of the differential equation y" + 2y' + 4y = e* sin 2x + æ?

A: the given equation is  y''+2y'+4=exsin2x+x2 Auxiliary equation corresponding to the equation is…

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A: Consider the provided D.E,

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A: Let's find.

Q: (c) xy' = y(3– x)

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Q: Solve the differential equation dr + x² + y², dy = 0. r² + y? y?

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Q: 1. Form the differential equation by eliminating the constant A and B from y = emx (A cos nx + B sin…

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Q: a) Solve the differential equation UTM dy dr sin z y", y(7) = 0. UTMU UTMUTM UTM

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Q: 2. Form the differential equation from the circle passing through the origin having their centers on…

A: This question is based on forming differential equation by eliminating constant.

Q: 1) y = c x2 2) y = ce* + c2e¬*

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Q: c) y' = -y2e* d) y' = y2 - 4

A: Use the variable separable method to solve.

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Q: y" + 4y' + 5y = 260e-t sin (3t)

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Q: 3) Given the differential equation xy" +4y --y=0. a) First convert the equation to a Cauchy-Euler…

A: The answer is given as follows:

Q: C) The dependent variable y is missing in the given differential equation. Solve the equation by…

A: To solve the given differential education.

Q: form the differential equation corresponding to (y – b) = 4(x -a) %3D

A: Given: The equation is (y-b)2=4(x-a)   To determine: The differential equation from the equation…

Q: Do the functions y₁ = cos5t and y2 = sin5t constitute a fundamental set of solutions of the…

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Q: Form the differential equation Por the curve y= 2sin (x + 3)

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A: Given ODE : (x2-1)dydx+2y=(x+1)2 ⇒dydx+2yx2-1=(x+1)2x2-1⇒dydx+2yx2-1=x+1x-1 Which Linear…

Q: Solve the differential equation: xy' = y+16/16x² + y² , y(1)=0

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Q: Find the order and the degree of the differential equation cos x COS X A 2,4 B) 5, 8 © 5,4 5,2

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Q: 9 y" – y + ម = ( a + 3)e-x

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Q: The functions g(b, c, d) and h(b, c, d) are defined as: g = (b+ c+ d')' + (b' + c' + d') · (b' . c'…

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Q: b) Form the differential equation from the function x = Acos(nt + a). e) Given that y = eax sin bx,…

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Q: Find the ordinary differential equation of a circle which passes through the points (0,0) and (2,0).

A: We will find out the required differential equation for given circle.

Q: 2. Form the differential equation having y=(sin-x)²+ A(cos-lx)+B. where A and B are arbitrary…

A: Introduction :