Is y directly proportional to x? y = 14x-8x If so, give the constant of proportionality. If not, enter NA. k =

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Q: 8. The volume of a cone (V) varies jointly with its height (h) and the square of its radius (r). If…

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Q: What is the integrating factor for the linear equation x*y + xy = sec x? A)I (x)=x B)I (x)= x2…

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Q: Solve the following equation by using separation variable method: u(x.0) = S(x) u,(x,0)= g(x) 1>0…

A: Given ∂2u∂t2=c2∂2u∂x2, ux,0=f(x)                            (1)utx,0=g(x)ux(0,t)=ux(l,t)=0 Use…

Q: a- If w = x² + 2xy and x, y change from initial values (x = 1, y = 3) By amounts dx = 0.01 and dy =…

A: Given: w=x2+2xy So, dw=2x dx+2y dx+x dy...(1)

Q: h is jointly proportional to q and v. It is found that q = 9 and v = 8 when h = 3. k =

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Q: If z is directly proportional to the product of x and y and if z is 10 when x is 4 and y is 5, then…

A: To determine: The equation z=_____ Given information: If z is directly proportional to the product…

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Q: The integrating factor of the equation (xlnx)y' + y = 2lnx is || Select one: a. ex O b. Inx c.…

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Q: b) Use method of variation of parameters to find the general solution to the equation x²y" – 3xy' +…

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Q: Solve the following equation and find the solution y as a function of x and C (constant of…

A: We have observed that the given differential equation is a first order separable ODE. So, by…

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Q: Suppose that z varies jointly with the cube of x and the square of y. Find the constant of…

A: Given z varies jointly with cube of x i.e x3 of y i.e y2

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A: Solution: The objective is to find the integrating factor to the given differential equation.

Q: In integration combination is equal to... ay2 ady-ydu A.d(x² + y*) B.dAretan (2) C.dArctan (E)…

A: Integration combination

Q: + Use Separation of variables to solve eくX<| Us co,t)こ0 I4 pts] ULx,0) = X

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Q: For the equation x’(t)+xcost = g(t), What is the integrating factor?

A: The integrating factor for given differential equation is

Q: B. Solve the following equation using the determination of integrating factors. 2. y(4x + y)dx –…

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Q: Solve the general solution using the integrating factors by inspection  2xydx + y²dy = x²dy

A: Tt

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Q: Solve the given equation using an integrating factor. Take t &gt; 0. i)  y′ + y = 1

A: Given: y'+y=1 To Find: To solve the given equation using an integrating factor

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Q: If y is directly proportional to x ,and when  x=20 then y=40 . what is the constant of…

A: It is given that y is directly proportional to x . That is,  y∝xy=kx Here k is the proportionality…

Q: = P + csc- 10. %3D dx x х

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Q: Solve y' + 4y/x - x³ y? = 0 12 Find the general solution. What is the integrating factor?

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Q: Express the statement as a formula that involves the given variables and a constant of…

A: Two or more variables are said to be directly proportional if a change in one variable results in a…

Q: Suppose that z varies jointly with the cube of x and the square of y. Find the constant of…

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Q: Suppose that z varies jointly with the cube of x and the square of y. Find the constant of…

A: Here, give that z varies jointly with a cube of x and the square of y. That is: z=kx3y2...(1)

Q: (10) Solve the given BVP by using Green's function: ; (ii) y" – y/ = e2; y(0) = 0, y(1) = 0

A: Given differential equation is: y''-y'=e2x y(0)=0y(1)=0 Green function in equation is given by:…

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Q: Use the method of successive approximations to solve the I.V.P y' = y(1– 2x), y(0) =1.

A: Given The given I.V.P is y'=y1-2x,         y0=1. Apply Picard's formula or successive approximation…

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Q: Find the constant of proportionality k if y = 2 when X = 8. %3D k = Using the k from above write the…

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A: We can solve the question as below

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Q: what is an integrating factor u(miu) for a linear equation y'+t(t)y=q(t). How do you find it…

A: We have to write integrating factor for given linear differential equation-

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Q: Identify the equation as separable, linear, exact, or having an integrating factor that is a…

A: Given,         2x+2ydx+2x-2ydy=0.

Q: y^2dy=x(xdy-ydx)e^x/y solve using homogeneous equations (diff eq)

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Q: Show that the following equation is homogeneous and then find the general solution. か_デー y -xy dx…

A: We have given differential equation ,  dydx = y2 - xyx2 - xy Here , fx , y = y2 - xyx2 - xy Now ,…

Q: If the rate of change of Q is directly proportional to Q, and if Q(0) = 100 and Q(4) = 440, find k,…

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Q: D³y = 0 ; x = 1; y = 1; y = 3; y" = 2

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Q: An integrating factor of (xy? – x?) dx + (3x?y² + x?y – 2x³ + y?)dy = 0 is A) ey B) ебу 1 C) 6y e D)…

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.