cost dt is a solution of the first- Vt (ii). Show that the function y = Vx Jª dy order ODE 2x dx I of validity of solution. - y = 2x cos x. Assume an appropriate interval

Q: dx xt x(1) = 2, solve for x(2) when h = 0.1 %| dt t²+2

A: As per the question we have to solve the following first order differential equation : dy/dx =…

Q: x*cos(y/x)*dy/dx = y*cos(y/x)-x   find solution of that differantial equation.

A: Let us consider the differential equation of the form dydx=fyx  then to solve the differential…

Q: Q3\ using Euler method, find an approximate value of y corresponding to x€ [0 -0.7], Given = x(x +…

A:

Q: (test for exactness) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xyev" )dy %3D

A: Given DE is 2ysinxcosx-y+2y2exy2dx=x-sin2x-4xyexy2dy Test the exactness of the given DE.

Q: Sinx 19)Let E(x)= Itt" dt for X in (-oo, co). Find F'X)

A: Explanation of the answer is as follows

Q: 1 dx dy A point is moving along the graph of the functiony = such that = 4 centimeters per second.…

A:

Q: Solve ODE for general solution: (2ysin(x)cos(x)-y+2y^(2)e^(xy^2))dx=(x-sin^2(x)-4xye^(xy^2)dy

A: Hence the given ode is exact. Obtain the general solution as follows,

Q: dx 4-t x(0) = 1, solve for x(0.5) when h = 0.05 %3D dt t+x

A: As per the question we have to solve the following first order differential equation : dy/dx =…

Q: dy at t = a where dt Find f(1+ vu), u = 2-x? and f'(2) = -3.Find dy when x = 1. dx 8. Let y ||

A:

Q: Solve dy / dx = 1 /( x^2 – 1) , for y(0) = 0. Find its maximal interval of existence %3D

A:

Q: The value of dy/dx for implicit function xy – x + y - 2 = 0 at point x = 1 is ... Nilai dy/dx untuk…

A:

Q: Q3 using Euler method, find an approximate value of y corresponding to xe [0 - 0.7], dy Given = x(x…

A:

Q: Exact DE se: he particular solution of (x + y)dx + (x – y)dy = 0 when x = 1 & y = 1.

A:

Q: f(x)= (ex+2 +1/e-x -14ex+1) / (xex-ex/x+1 +lnee^x) differentiate?

A:

Q: dx 1. dt xt x(0) = 1, solve for x(0.3) when h = 0.1 I| -

A: Given function is, dxdt=-12xt,   x(0)=1, h=0.1 and we need to solve, x(0.3)   Here we have, (t0,…

Q: dx 9. J, 16 Vx - 2 3 10. x V9- x dx 11. [ sinycos ydy dx 12 J. (x – 3) x- x 13. [ x +x

A: Use substitutions to integration

Q: (b) Using Runge-Kutta forth order method, find y for x = 0.1 and x = 0.2 of the initial value ODE =…

A:

Q: dx 2. dt x(0.5) = 1, solve for x(1) when h = 0.1 2(t+1)

A: It is given that, dxdt=x2(t+1),    x(0.5)=1, h=0.1 and we have to find x(1)   Here interval is 0.1,…

Q: Dse Runge - kutta method to Solve the equation: dly x +y %3D dx at x =0.8 given that using h= o.4 y…

A:

Q: order differential coefficients as serie (b) y) when y = (7) sin 50. 50

A:

Q: Q6: Use classical fourth-order RK method to solve the following problem over the interval from x= 0…

A:

Q: Linearize given function at point and fin an error upper bound xy + y cos (x – 1) at Po (1, 2), take…

A:

Q: 10. f (x, y) = 1 sec(xy) in(rv)

A: Solution:-

Q: blve using method of undetermined coeffi cients d x X.P + 6 dx dt 3 + 12 dx + 8x =0 dt2 dt when t…

A:

Q: Can you help me step by step?

A: Differentiating the given equation:

Q: g) y² ex+y = cosh x + √rosh²x -1 +7 et h) (3 x y² + 4y) dx + (3 x²y² + 2x) dy = 0 I) sin x dy Sin 2x…

A:

Q: Let y = tan(3x + 2). Round all answers below to 5 decimal places. Find the differential dy when x =…

A: Given, y = tan(3x +2 ) So,  dy/dx = sec2 (3x +2) * 3          (because d[tan(ax + b]/dx = sec2[ax…

Q: dy dx Assume x and y are functions of t. Evaluate for 4xy -3x + 5y° = - 210, with the conditions dt…

A: Given: 4xy-3x+5y3=-210 with the condition dxdt=-15, x=5, y=-3 To find: differentiate the given…

Q: ;+ 2リ+y = ハ- cos(t) Slove the D- E t2 with. Ze Vo initial cuudition s En gineer ing Analysis

A:

Q: 11. Integrate the function. y? dy (49 – y²) 7y y + C V49 – y2 – sin y+C -1 - V49 - y2 | O A. O B.…

A:

Q: Let y tan(3x + 2). Round all answers below to 5 decimal places. Find the differential dy when x = 2…

A:

Q: 2 Approximate 0.5źdx using trapezoidal rule. X-4 Select one: a. -0.02678571 b. -0.2276571 C.…

A:

Q: #@3 g (x1y) =- 7x3 -49xy + 7y3 Find and elassify all the extrema of the fine tion

A: Given- gx,y=7x3-49xy+7y3 To Find- All the extrema of the above function. Concept Used- Using the…

Q: Q4. Test for exactness and solve (ycosx – cosy)dx + (sinx + xsiny)dy = 0

A:

Q: Solve using separation of variables xy^2 dx + e^x dy = 0; when x -> infinite, y -> 1/2.

A:

Q: h'(x) = cosxcot(sin^3x)+cosxsinx ⠀ h(x) = sin(x) -2 (cos(t³) + t)dt

A: Applying Leibniz's rule

Q: Q3\ using Euler method, find an approximate value of y corresponding to X€ [0 -0.7], Given = x(x +…

A:

Q: e) cos (x + y) - cos(x - y) =-2sinxsiny

A: The LHS of the given equation is cosx+y-cosx-y. Note that, cosA+B=cosAcosB-sinAsinB and…

Q: 01 ation. Solve (1-x²)x+m²y=0 dx where x = 0, y=0, dy- dx

A:

Q: Evaluate the integral. cost dt sin n² t - 5 sin t + 4 Select one:

A: We will substitute sint=x, then we will do partial fraction.

Q: y2 Use the modified Euler Method to solve the ODE = dx subject to y = 1 when x = 0 1+x on the…

A:

Q: dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II

A: From the above question, we get the differential equation dydx=-a2-x2x with the initial condition…

Q: Beta Function x dx 3/3 dy (h) 1+ 142/2 that (a)

A: In the given question, the concept of the Beta function is applied. Beta Function is expressed as-…

Q: Find the value of dz and 8z/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A: Given  data  xey+2z-cos(xy)+ey-ln2=4  ,  A(ln2,0) Also given  when x changes by (dx=0.01) and y…

Q: II. Test for exactness. If it exact, solve. 1. (x- 2y)dx – (2x + 5y)dy = 0 2. (4x³y-18x² + y)dx+ (x*…

A:

Q: (3x2y+2e2y+3)dx + (x3+4xe2y-sech2y+2lny-y)dy=0

A:

Q: 1. Solve for y3 using the method of successive approximation. dy =x+ y; y(1) = 1 dx %3D

A: The given problem can be solved by the following method,

Q: let's consider the equation (2xy - sec2 x) dx + (x2 + 2y) dy = 0

A: