1 Given: y = 4x4 Find: y' 4x4

Q: 3. Using Euler's method, find an approximate value ofycorresponding to x= 1.6, given =y -and dx y =1…

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Q: Solve the given dif fential by variations of parameters 2.y" + 2y + y = e Int

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Q: r3 V9-x² »6-x-y dz dy dx in the order dz dx dy 0,

A: Given triple integral is ∫03∫09-x2∫06-x-ydzdydx

Q: , X= sin ztS d= In Find dw 2- Cost

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Q: 2. Use the composite trapezoidal rule with the step length h = 0.1 to evaluate dx I = 1+x2 and…

A: Composite trapezoidal and composite Simpsons 1/3rd rule

Q: EVaLuate W= X -*-cos't ,y=cost sint

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

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Q: Q1/ Evaluate So (x² + 3y²) dy dx using Simpson's 1/3 rule in x-axis and Simpson's 3/8 rule in y axis

A: 1 Given integral is ∫03∫01x2+3y2dydx. We have to evaluate the given integral  by using Simpson's 13…

Q: Please utilize Method of Variation of Parameters. Find the general solution: y" – 2y" + 4y' – 8y =…

A: We have the following third order linear non-homogeneous differential equation : y''' - 2y'' + 4y'…

Q: B: By using Homogenous method solve the first order differentia еquation (1+ e») dx - e"l> -1) dy =…

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Q: Used range Kutta method to find y(1) if y (0) = 2 dy x+4 + cos y+5 dx

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Q: dy = 9 +y osx dx

A: Given

Q: Solve using method of variation of parameters. 6. y" + 3y' + 2y sin(e*)

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Q: Find the solution asked using the process of Homogeneous. (16x + 5y)dx + (3x + y)dy = 0; the curve…

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Q: dy 3 sinh y - 5 cosh y

A: Given, I=∫dy3sinh y-5cosh y

Q: If y = 4x³ + 2x² + 11, find the approximate value of y when x = 2.01, using differentials.

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Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate (x' + 1)dx.

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Q: (2х — Зу)dx + (2у — Зx)dy %3D 0

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Q: 2x dx by taking n = 4 1+ x Use trapezoidal Rule to evaluate

A: trapezoidal rule

Q: 5. Find the particular solution (IVP) for the DE below: a) dx +2 =8x when x = 2, y = 6 b) 3y2 = 2x +…

A: Use variable separable method

Q: (3sin y– 5x)dx+2x² cot ydy = 0 3.

A: Given: 3siny-5xdx+2x2cotydy=0

Q: Solve y at x = pi/3. cotx dy/dx = 1 - 2y, y(pi/4) = 1 0.75

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Q: Solve using the integrating factors by inspection (y²-3-x) dy + ydx =0

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Q: 9. Find dy for y defined implicitly. by the equation xy-secly)-3x

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Q: 1.(x fan y t y) dx - xdy = 0 2- ye "dx - (ure)dy cbssitication and Solution by appropiate methed

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Q: = y² dy dx

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Q: Solve the DE using Variation of Parameters: y"+y = sec' x %3D

A: Given  The differential equation using variation of parameters. y''+y=sec3x

Q: Solve by integrating factors found by inspection: y (x2 - y2 + 1)dx - x (x2 - y2 - 1) dy = 0

A: To solve: y(x2 - y2 + 1)dx - x(x2 - y2 - 1)dy = 0 ⇒yx2 dx- y3 dx+ y dx - x3dy +xy2dy +xdy = 0

Q: finel cly 0- ó cost +1nt) e e (cos Ø + Ssin ø)

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Q: 1 Evaluate dx by using Trapezoidal rule. Hence obtain 1 + x2 he approximate value of .

A: I am attaching image so that you understand each and every step.

Q: Find the differential dy. y = cubic root of 3x^2

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Q: Find the differential dy for y = xV1-x. Do not simplify your answer.

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Q: 2x dx by taking n = 4. 1+x Use trapezoidal Rule to evaluate

A: on solving this we get

Q: 10. use "Bernoull's Equation" method dy -y= ey! dx

A: The given problem is to solve the Ordinary differential equation using Bernoulli equation method, we…

Q: dy of y=X Find

A: y = x^x Find dy/dx

Q: Use Euler's Method to approximate y(10.8) with step sizeh 0.2. dy = 3y + x- 5 y(10)= 0 %3D dx

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Q: Use Euler's method to estimate y(0.02) ey-x y' = 1+e3y „y(0) = 4 0.01) What is the error in the…

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Q: Find dy by dx where y is equal to x cube under root 1+x²

A: We know that, for two functions u(x) and v(x), ddx(uv)=vdudx+udvdx Also, ddxxn=nxn-1.

Q: 8. Find dy/dx in terms of x and y using implicit differentiaton 5y 4 +x 2 = 9

A: Step for implicit differentiation: (1) Differentiate with respect to x (2) Collect all the…

Q: 9. use "Bernoulli's Equation" method (ye-+y)dx-e-dy 0

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

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Q: Use Euler's method (with all details) to find approximate value of = 2y - 2x² -3, given that y = 2…

A: Given: y'=2y-2x2-3 , y(0)=2 , h=0.3. We find y(3) by using Euler's method. The formula for Euler's…

Q: Solve using the integrating factors by inspection and get the general solution of…

A: The given differential equation is, yx2y2+2dx+x(2-2x2y2)dy=0 Now rearrange terms as below:…

Q: Use the method of isoclines to draw several solution curves for the equation: dy/dx = x/y

A: We can use isocline lines to draw constant slopes along that line. Using some (at least four but six…

Q: Find the general solution of the equation dy + (tan t) y = cost dt

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Q: Q2. Find of y = 4x/x + V at x = 1? dx

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Q: y

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Q: Use Euler's method to estimate y(0.02) ey-x y' 1+ e2y »y(0) = 1 (h=0.01) .What is the error in the…

A: The solution is given as