Choose two of the following DE and test for its exactness to obtain the general solution or particular solution if possible. 1. (v² – 2xy + 6x}dx – (r² – 2xy + 2)dy = 0 2. 3y(x² –1)dx + (x³ +8y – 3xdy = 0 when x=0, y =1

Q: . solve for y(3) at h =1.5, given y(0)=5 using heun’s equation and euler’s method dy dx = 3e −x −…

A: Heun's method: Heun's method also known as Euler's modified method. It works in following steps. 1.…

Q: Find ø(2) for a solution p(x) to the initial value problem: 2y dx = (x2 – 1)(dx – dy); y(0) = 0 %3D

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Q: Solve the initial value problem dx 2x cos(4t) - dt with x(0) = 1. x(t) = = sqrt(-1/4sin(4t)+1) Hint:…

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Q: (2a+1) 5. S -dx (z+2)*(x–1)*

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Q: Q5: Solve by using Modified Euler's Method. dy = x + cos(y) ;0 <x<1 ;y(0) = 1;h = 0.5 dx

A: Given the DE is dydx=x+cosy,0≤x≤1,y0=1,h=0.5. The modified Euelr's method is defined as follows:…

Q: Consider dy – y sin(3x) dx = 0, y(0) = 1, x € [0,1] a) solve this problem using RK4 with step sizeh…

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Q: 04 (test for exactness) (2xsinycosy - x+2x?evx* )dy =(y-sin?y -4xyex )dx 04 (solve de) (2xsinycosy -…

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Q: obtain the general solution.  dx =t(1+t2)sec2xdt. (1+In x)dx+(1 +In y)dy =0

A: (1). The given differential equation is: dx=t1+t2sec2x dt

Q: Q5: Solve by using Modified Euler's Method. dy = x + cos(y) ; 0 < x <1 ;y(0) = 1 ; h = 0.5 dx

A: Disclaimer: We use the modified Euler's method to solve a first-order ODE and find the value of the…

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: Solve for the given DE: y(y^3-x)dx+x(y^3+x)dy=0

A: first we will check this is exact or not this is not exact then we will find its integrating factor…

Q: 1. Test for exactness and determine the particular solution of: (yexy – 2y³)dx + (xe*y – 6xy² –…

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Q: 2.ly-x dx+ dy = 0

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Q: 2. Obtain the general solution using Bernoulli's equation. Si l + x/ dx – 6x dy = 0

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Q: 3. Is the expression (ez+y+z +4x²y²2²)dx+(e²+y+z +r’yz²)dy+(e²+y+z+³y²z)dz = 0 %3D exact? If yes,…

A: Given expression is ex+y+z+4x2y2z2dx+ex+y+z+83x3yz2dy+ex+y+z+83x3y2zdz=0 To verify whether the above…

Q: Q1: Solve by using Euler's Method. dy = x + cos(y) ;0sx<1 ;y(0) = 1 ; h = 0.5 dx

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Q: Show if the the initial value problem is dy separable or not -=y²(1+x²) • dx vith the initial value…

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Q: Given that dy/dx = 2 +underroot(x+y) , y(1) = 1. Find the value of y at x = 2 in steps of 0.1 using…

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

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

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

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Q: 1. y = √2x +7 2. y = √7+√√3x + 1 3. y Arctan√1-x²

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Q: Test for exactness and determine the particular solution of: (yexy – 2y³)dx+ (xexy – 6xy2 – 2y)dy =…

A: As per our guidelines, we are supposed to solve only first question. Kindly repost other question as…

Q: 1. Obtain the particular solution when x = 1 and y = 1 5) dx 3 + y 3 dy = 0 y

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Q: Q1: Solve by using Euler's Method. dy = x + cos(y) ; 0 <x<1 ;y(0) = 1 ; h = 0.5 dx

A: If dydx=fx, y, yx0=y0 then Euler's method states that  yn+1=yn+h·fxn, yn Given : h=0.5, x0=0, y0=1,…

Q: Q1\ Use Runge-Kutta method with (h=D0.1) to solve the equation y+ 3xy - 6y = 0 ; given that yo = 1…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the particular solution of the equation 2(x +3) dy – xy dx = 0 %3D - tisfying the initial…

A: Given: 2(x+3)dy-xydx=0     satisfying the intial condition x=-2 and y=1

Q: 3. Solve (2xy – y² + y)dx + (3x² – 4xy + 3x)dy = 0. (Non Exact) 4. Solve the following FOLDE: (2у +…

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Q: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

A: Given: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

Q: Find general solution of (x − 4y − 3)dx + (−x + 6y + 5)dy = 0 (DE WITH COEFFICIENTS LINEAR IN 2…

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Q: 4. Using homogenous D.E approach, solve (x³ – Зху?)dx %3D (у3 — 3x2у)dy. (v³ – 3x²y)dy. | 2 (ardai…

A: The given differential equation is; (x3-3xy2)dx=(y3-3x2y)dy.

Q: (4x*y³ + }) dx + (3x*y² –-;) dy = 0 for x(e) = 1 %3D

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Q: dr2 dx dx d²y, 7 dy , 9y 3. dr2 dy =1 at x = 1. dx = 0; y = 0 and x dx x2 4. Use the method of…

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Q: Q20// when x3+y3+x?y xy2+x3 dy %3D dx find the general solution?

A: Given differential equation is  dydx=x3+y3+x2yxy2+x3 the given differential equation is homogenous .

Q: 6) 3x²y dx + (x² + y²) dy = 0 3

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Q: 4. Find the general solution of this DE using INSPECTION. dadx + aydy +(X² + y?)dx = 0

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Q: 16. 1) Given that y+x-2y 0, find in terms of x and y. dx ii) Given that x =t'. y 1/t, find in terms…

A: Derivative of implicit and parametric function

Q: dy 2. 32 +5y = sin x, y(0.3)=5 and using a step size of h = 0.3, Approximate the value of y(0.9) dx…

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

A: We have to find y3.

Q: Trapezoidal (Use n = 9) 3 5. S¹ (5√x-³) dx √x 6. √² (5ex - e)dx

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Q: 14. Obtain the particular Solution by satisfying the conditions indicated. (x - y) dx + (3x + y) dy…

A: Put y = vx

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: Find the general solution of : x tan²y dx + (1+ Vx ) dy = 0

A: To find the general solution of : x tan2y dx+1+xdy=0

Q: = x²y - 1.1y dx using (a) analytical method, (b) 3rd-order to 5th order RK Method with h = 0.25 and…

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Q: 8

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Q: 8. a) Solve by Picard's method dy = 1+ xy, dx y(0) = 1 for x=0.1. Compare it with the exact value of…

A: Here given differential equation is                                                     dydx=1+xy,…