Example find y (1) if dy y (1) if dy = 1/(x-Y) ; Y(0) = 1 dx (Use h=1) using Eulers method and using Runge kutta 2 and 4th order methods, write your results in tables and compare the results with the exact solution ?

Q: dy Find when y = a dx (a) (b) (c) (d) 2bx x4 + b² Arctan Arctan(2) 2bx ln a _ Arctan x4 + b² x In a…

A: Given y=aArctanbx2

Q: (a) Write the equation in slope-intercept form, and determine the slope and y-intercept. (b) Graph…

A:

Q: Solve y (e* + Inx) dx + (3 – y) dy = 0

A: The given ordinary differential equation can be written as:

Q: dy 1 csc(x) -csc(x) y = y* dx

A:

Q: Q/find (2xy? -2x² y4 xy2+2x)dx+(3X=y?e4yldyco an int egratinagfactor theequation and find the…

A: Given the first order differential equation           2xy3-2x3y3-4xy2+2x dx+3x2y2+4y dy=0 Find the…

Q: How does d/dx(xy^2) work?

A: To find the value of .Concepts used:Product Rule of Differentiation: .Differentiation formula: .The…

Q: dy/dx= (6x^3-1)/(2xy-3x), y(1)= -1, x>0 Please show steps clearly, this is a seperable equation…

A:

Q: (xy² + x)dx-(x²y-y)dy = 0, y(2) = 5.

A:

Q: +8x-x +2x +1 (x² + 3)(x' +1)

A: SImplification of the given function helps to find the required integrated function. The partial…

Q: Find linearization of the given function: f(x) = 1/x at x=0.5, dx = 0.1 %3D

A:

Q: 3x(xy - 2)dx + (x³ + 2y)dy = 0; f(1)=2 Find the positive root of y at x=2. Use 2 decimal places.

A:

Q: y = arccos /1 – x (1-x) 2 1 (1-x) 2 2 JA (1–x) 2 1 (1–x) 2

A:

Q: y" – y' – 30y = 0 0) - 1, у 10) --4

A: The general form of a second-order homogenous linear differential equation is given by…

Q: f (x) = ƒ a + bt + ct²dt 2 f'(x) = x²(2x³ – 3x) + 4x - and calculate: a +b+c=?

A:

Q: (3) (2x – 3y – 2)dx + (6(2x – 3y) – 2)dy = 0. - - %3D

A:

Q: lIf 90 +9f(x) + x²(F(x))* = 0 and f(3) = -2, find f'(3). f'(3) = %3D

A:

Q: x²e-3x dx

A:

Q: dž 3 9. with x(0) = dt -1 -3 x1(t) = help (formulas) x2(t) : help (formulas)

A:

Q: A linear model of the spread of an epidemic in a community of 1000 people is the equation: dx/dt =…

A: To find the number of people x(t) who have contracted the disease at the time oftime t.

Q: Differentiate the function and simplify the answer. f(x) = 2x e2r'+x² Select one: f'(x) = 2xe2r³+x?…

A:

Q: 2dy+ydx=y3(x-1)dx (Bernoulli)

A: We have to find the general solution of differential equations

Q: 4 xf (x* )dxif f(x)dx = 5. Find Enter the exact answer. f (x* )dx=

A: given:-∫04f(x)dx=5now∫-20xf(x2)dxlet,x2=t2xdx=dtxdx=12dtx=-2,    t=4x=0 ,       t=0

Q: If y=x^(2)+81, find the relationship between (dy)/(dt) and (dx)/(dt) Where x,y depend upon t.

A: We have to find the relationship between  and where  and  depend upon .We use Chain Rule to answer…

Q: (2xe + e*)dx + (x² + 1)e'dy = 0

A:

Q: 7. 1. f(x) = 6 /x? - 20 x + 4 find f (4) (x). 收 .5 2. x-xy+y 3, find y".

A: 1) fx=6x23-20x45+7x57+4x6fx=6x23-20x45+7x-57+4x-16Differentiating with respect to…

Q: Solve the following differential equation: yde+xdy 1-x²y² +ædr=0. = constant.

A: Given that the differential equation ydx+xdy1-x2y2+x dx=0

Q: Let f (x) = x - 1 and g (x) = x² (x + 1). Evaluate Se 3 + dx f(x) g(x) You must show all steps.

A: Integration of e-3x+f(x)/g(x)Where f(x)=x-1,  g(x)=x2(x+1)

Q: Find all solutions to the equation (D^2 − 3D + 2)y(x) = 2e^3x.

A:

Q: Pick the equation that matches the graph below |– x^ Vx 1 O = Vx + 1

A: Given query is to find the equation of the graph.

Q: t (x) = e – 3x +2 | Find Where Increasing/Decreasing

A:

Q: Find a > 1 to express y = 3(2/9)x in the form y = 3(a−x)

A:

Q: Estimate the value of df/dx for f(x) = root 8x at x = 3, using any method

A: To find the derivative of f(X), differentiate with respect to X on each side.