I. Identify whether the given equation is linear or non-linear (Xie, 2010) 2. x=2- dy = 2- d²y dx2 dx 3. Зуу'у" - у3 +1%3D0 4. y(6y2 – x – 1)dx + 2xdy = 0

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Q: a) Find the general solution of the given equations of the line (2x - 5y + 10)dx+ (7x + 3y - 8) = 0

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Q: Find the equation of the curve that passes through (2,3) if its s dy = 5x-7 %3D dx y(x) =

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Q: I. Identify whether the given equation is linear or non-linear (Xie, 2010) 1. xy' = y + Jx² – y2 2.…

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Q: (x + y – 2) dx + (x – y + 4) dy = 0 |

A: Given:-(x + y - 2) dx + (x - y + 4) dy = 0To find: Find the family of equations

Q: Find the general solution for the equation dy/dx=(2x/y)e^y+2x

A: Given the differential equation, dydx=2xyey+2x    ⋯⋯(1) Rewriting equation (1),…

Q: Solve the equation dy, 3y + dx +2 = 3x, y(1) = 1.

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Q: y'=loga (Zy -4y +5) %3D by U =Zx-4y +5 7(2)

A: If we want to change the variable of the differential equation for find solution easily from…

Q: 4. у(бу? — х — 1)dx + 2xdy — 0 -

A: This is non linear equation. Since y is dependent function which is non linear form.

Q: The solution of (y + x + 5)dy = (y – x + 1) dx is %3D

A: An ordinary differential equation is an equation containing independent variables, dependent…

Q: Find the general solution of = 8e-4x %3D dx

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Q: If x1/3 + y1/3 = 4, find d2y/dx2 at the point (8, 8).

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Q: Classify the equation as separable, linear, both, or neither.

A: ydydx=2x+y

Q: C. Find the value of dx/dz&dx/dy y lnx-x² + 4 = 0 at the point (1,-1,-3) if the equation xz +

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Q: y' = 5y + y?

A: First we convert the given Bernoulli equation into linear differential equation. After that we…

Q: Solve : (6x + y) dx + y(2x – 3y)dy = 0 xự + 3x? – = c 3æy – 3x? – y = c | - Option 1 Option 2 xy +…

A: We have to solve

Q: Solve and specify method used. x dy y dx х3 dx y2

A: Given DE is (x dy - y dx)/y2 = x3 dx  We solve this DE and we specify the method used.

Q: dy 2x = (3y + x)- dx

A: Given, 2x=(3y+x)dydxdydx=2x3y+xPut y=vxDifferentiate…

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Q: Find the equation of the solution to dy/dx=x4y through the point (x,y)=(1,5).

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Q: dx Vx-4x-7 S- -dy y2-8y+5

A: The given integrals are' 1)1/sqrt(x2-4x-7)  2)7/(y2-8y+5).

Q: Find the general solution of the followin d² y equation 5 + 4y = 8 +5. dx2 dx

A: General solution is sum of particular integral and complimentary function.

Q: The equation (x*y^2 + x - 2y + 3)dx + (y*x^2)dy = 2(x+y)dy is not exact. true or false?

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Q: Find if-10x – 6y = -6. dx2 Provide your answer below: %3D dx

A: We Have to find second order derivative

Q: I Determine the order and degree of the differentiah equation dx y-

A: As per our guidelines we are allowed to answer only one question. Kindly repost the other question…

Q: If xy3 + x3y = 2, find dy/dx at the point (1,1). a. 1            b. -1 c. 2             d. -2

A: Given that:-xy3 + x3y = 2To find : dy/dx at the point (1,1)Differentiation rules:power rule:…

Q: (D5+ D4-7D3³ - 11D²8D-12)y = 0

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Q: 1 -y y 2 e dxdy

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Q: If we take an adequate substitution, the following Bernoulli's equation y' +y = -x°y%, will be…

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Q: determine the general solution of the equation. x(y'-x)dx-y(y'+x)dy=0

A: we will integrate this equation and find the solution of the equation

Q: Determine whether the equation (3x + 2y)dx + (2.x + y)dy = 0 is exact. Find the solution if it is…

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Q: хdу — dy %3D (3x? — 3х)dx — ydx

A: The solution is given as

Q: Please solve (2x-y)dx + (4x+y-3)dy = 0 using Linear coefficient method.

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Q: Find at the given point without eliminating the parameter. dx2 1?, y = , X = 2 t = 2 3

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Q: dt? + 7Q = 0 dt

A: we have to solve the differential equation d2Qdt2-5dQdt+7Q=0

Q: If y-2xy 21, then dy dx at the point (2,-3) is

A: We have to find dydx at the point 2, -3 for the equation or expression: y2-2xy=21 We know the…

Q: How / Find the solution for the equation @ y√ √ x² + y ² dx = x (x + √x² + y²) dy 1

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: If x^(1/3) + y^(1/3) = 4, find d2y/dx2 at the point (8, 8).

A: Applying derivative for the given equation with respect to x:

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Q: A car is driving away from the base of a 30-meter-tall building. y 30 metres Car (a) Which of the…

A: We have given right angle triangle  Using Pythagoras theorem  (Hypotenuse)^2 = (Perpendicular)^2 +…

Q: If A = 4x³ and (a) TRUE (b) FALSE dt dx 2, then dA dt = 150.

A: As we know the Power law; ddxxn=nxn-1 Given: A=4x3 and dtdx=2

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Q: 3. 2X dy 2. %3D

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Q: If x+y = 63, find the value of dy at the point (-1,4). %3D dx2 The value of at the point (-1,4) is|:

A: Given, x3 +y3 = 63  We have to find the value of d2ydx2 at the point -1, 4.

Q: Solve by substitution of u = Ax + By +C  dy/dx = (x + y +3)2

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Q: Find, the, general solution of 2 dy + y = xe"Inx. dx²

A: Given the differential equation           y''-2y'+y=xexlnx Find the general solution.

Q: If 2x2-3y2=5xy, then find dy/dx | x,y=(2,-4)

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Q: Obtain the general solution to the equation. dx 8 y: + 4x = 9y dy

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