Q3: van fy = xy-1+ x.ln(x) J f(x,y) = x' + y* if it was

Q: Find the differential dy for the given values of x and Δ x. y = 5x 2 - 2x + 3 ;  x = 2 , Δ x = - 1…

A: Given that: y=5x2-2x+3,  x=2  ,  Δx=-16

Q: 5. If the function y = y(x) is such that dy + 2y = x cos r, dr use the integrating-factor method to…

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Q: dy 2х + ху is separable. dx y2 + 1

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Q: How does the Fundamental Theorem provide a solution to the initial value problem dy/dx = ƒ(x), y(x0)…

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Q: (b) Solve the integral [(3x – y)dx +(2x +3y)dy along the curve x = y' from (0,0) to (1, 1).

A: Solution of question as follows

Q: Let y 5x? + 5x + 2. || Find the differential dy when x = 5 and dx = 0.3 Find the differential dy…

A: GIVEN: y = 5x2 + 5x + 2

Q: d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2

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Q: The integrating factor of the DE   y(2x - y + 1) dx + x(3x - 4y + 3) dy = 0 is

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Q: Find the particular solution, Using the integrating factor method: dy + In x =-y where y(1) = 3. dx

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Q: Let y=5x^2Find the change in y, Δy when x=3 and Δx=0.2Find the differential dy when x=3 and dx=0.2

A: To find the following parts. 1.)find the change in y (∆y), when x=3 and ∆x=0.2. 2.)find the…

Q: 3. Write the exact differential: f(x,y)=e-y-el-

A: Given- fx,y=ex-y-ey-x To write the exact differential.

Q: If f(x, y) = 3x² – 7y, then the total differential of ƒ at x = 1 and y = -2 is :

A: we need to find the total differential of the function  f(x,y) = 3x2 - 7y2 the total differential,…

Q: Q4/ 2x 1- If z = f(x,y) and z = x²y³ + + 1. Determine the total differential. -"/2 2- Evaluate: 2 S*…

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Q: (a) Find the differential dy. y = 1/x+1

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Q: Find the differential dy. (а) у — ху5 xv5 – x dy = (b) y = (1+x)-9 dy

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Q: Let y = 3x² + 3x + 4. ind the differential dy when x = 4 and dx = 0.4 ind the differential dy when x…

A: Given query is to find differential at given point.

Q: 7. Evaluate the improper integral. -kx e (k: constant)

A: Please refer to the image below.

Q: Let y = 5x?. Find the change in y, Ay when a = 3 and Ax = 0.3 Find the differential dy when x = 3…

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Q: (2? – 4)dy + (6x – 2xy)dx = 0 |– In x2- , where C is a constant of integration.

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Q: 4 2 1 Evaluate || - dy dx by reversing the order of the integration. O V Y +1

A: Given:∫04∫x21y3+1dydx

Q: If 9. 3. 6. f(x)dx = || f(x)dz + 6. what are the bounds of integration for the first integral?…

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Q: Find the generat Solution t dy (2y + xy) dx or Special o the differential * +1=

A: We have to find the general solution to the differential equation 2y+xydydx=1+4x+4x2

Q: 4. Given xy+x*y=2 such that d/dt =2 in/sec. Find dy/dt for x= 1

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Q: (b) Solve the integral [(3x– y)dx+(2x+3y)dy along the curve x = y³ from (0,0) to (1, 1).

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Q: What is the differential equation of the orthogonal trajectories of the family of curves y = Cx ? (A…

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Q: Find the differential dy of the given function. y = √√√√9-x²

A: Given y=9-x2 we need to find dy

Q: Find the general solution of the differential equa- tion / - a?y = -x - xy, %3D where |r| < 1.

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Q: х+1 y 2x 1

A: Given,            y = x + 12x - 1

Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

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Q: dy Use 4th order Runge - Kutta method to integrate step size of h = 0.5 and an initial condition of…

A: Let dydx=f(x,y) and the initial condition is y0=f(x0) . The 4th order Runge-Kutta method uses the…

Q: (b) Use the total differential dz to approximate Az. dz = X

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Q: Find the differential dy of the given function. y = Invs - x dy =

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Q: 1. Evaluate the integral r4-x² 8x cos Y dy dx Y – 4 by reversing the order of integration.

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Q: dy 4. y dx ;y(1) = 3 x(х+1)

A: In this question , Firstly we can integrate on both sides and solve the integral. After that we can…

Q: Find the change in y, Ay when x 1 and Ax = 0.1 Find the differential dy when x = 1 and dx 0.1

A: Let y=5x^3

Q: Find the differential dy for y = x2 - 4x + 6, then evaluate it when x = 2 and dx = 0.1

A: Differentiate the given curve y=x2-4x+6 w.r.t.  x use the power rule of differentiation i.e.…

Q: dy = (x – 2)e-2y dx einitial condition y(2) = In(2).

A: Explanation and solution is given below.....

Q: 8. Compute the differential df of f(x,y) = log (x² + y²).

A: Given; f(x,y) = log(x2+ y2)

Q: ve the given differential equati dy dx - (1 + x)y = xy

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Q: 8) Let z = y-x². Use differentials to estimate dz when x = 1,y = 5, dx = 0.03, and dy 0.1. !! %3D

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Q: The integrating factor of the DE (x^2 + y^2 + 1) dx + x(x - 2y) dy = 0 is

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Q: Find the differential of the function y = In(S - 2x) 2dx dy = (5-2x) dy = (5 – 2x )dx -2 (5-2x)dx…

A: Given : The function y = ln(s - 2x).   To find the differential of the function y = ln(s - 2x).

Q: Find the differential dy of the given function. Xx + 5 y = 2х — 9

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Q: So Sty dx dy √y(1+x²) The value of integration is very high

A: Given ∫01∫y1dxdyy(1+x2)

Q: 1. Evaluate the integral 2 4-x² 8x cos y y-4 by reversing the order of integration. dy dx

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Q: (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y =…

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Q: 1. Evaluate S Vx3 +1 dx dy by reversing the order of integration.

A: Given:

Q: (b) Solve the integral (3x– y)dx+(2x+3y)dy along the curve x = y' from (0,0) to (1, 1).

A: