After solving for the factors of dy/dx, the equation y*[(dy/dx)^2] + 2xdy/dx - y = 0 will reduce into which %3D type of first order ODE? а. Bernoulli O b. First-order ODES are not my type O c. Separable d. Homogeneous e. Linear

Q: The differential of y = (5x-6)e2z has the form | dy = (mx + b)e2# dz %3D Find the values of m and b.…

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Q: 6. Solve the following DE's using Integrating Factor by Inspection or by applying Table 1. y(y? +…

A: (1) The given differential equation is: yy2+1dx+xy2-1dy=0After simplification,ydx-xdy+y3dx+xy2dy=0…

Q: Given f(x, y) differential df = 10x?y then the total O 20xy dx + 10x² dy 20x dx + x2 O 2xy dx + x²…

A: For the solution follow the next step.

Q: Which one is an integrating factor for the equation y(2x – y+ 1)dx + x(3x – 4y+ 3)dy=0? 9020900 et

A: Given that, y2x-y+1dx+x3x-4y+3dy=0                               ……(1)   The above differential…

Q: The single Solution of the differential e quation y=Px+ Cas (P) a) (-Y +* sin'slu? b) (-y - X…

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Q: 3) 2xydy = (x³ + y²) dx

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

Q: Find an integrating factor that turns the following equation into exact and solve the IVP: (2xy3 +…

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Q: Find an integrating factor for the linear DE of order one dx + (2xy – 1)dy = 0. (1)y? ... (2) ev²…

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Q: (x² y3 + 2y)da + (2.x – 20° y²)dy = 0

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Q: (a) Find the differential dy. y = rad(15+x2) (b) Evaluate dy for the given values of x and dx. x =…

A: a)   The given function is y=15+x2. The differential of y is,…

Q: For a function y = g(x) the differential dy is given by:

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Q: (2xy + x? + x+)dx – (1 + x?)dy = 0 -

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Q: Given = y² dx - and y(1) = 1. Let h=0.2 Find an approximated value of “y" corresponding to x=1.6,…

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Q: If df = y(xy + 1)dx - xdy, determine if is a state function of the variables x and y, if not, what…

A: Here we have to check that df is exact or not

Q: Solve the following DE's using Integrating Factor by Inspection or by applying Table 1. y(y² + 1)dx…

A: (1) The given differential equation is: y(y2+1)dx+x(y2-1)dy=0ydx-xdy+y3dx+xy2dy=0Divide both sides…

Q: The exact differential d(xy)= xdy+ ydx , what is the d O= 4x²y°dy+ 2xy*dx.

A: Find your answer below

Q: dy = ( e )dx

A: See the attachment

Q: E valauate the JJ x +2xy +ydy dx when step size of x-0.2 and step size of use the Trapazaidal Rale…

A: given I=∫01∫02x2+2xy+y2dydx with  h=0.2 let x0=0.2 , y0=0.5 let fx,y=x2+2xy+y2 substituting the…

Q: a) Find the differential dy. y = ex⁄2 dy = ? (b) Evaluate dy for the given values of x and dx.…

A: Explanation of the answer is as follows

Q: (a) Find the differential dy. y = cos(Tx) dy = (b) Evaluate dy for the given values of x and dx.…

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Q: Find the solution of the following ODE: dy y + 1+x2 0, y(0) = 1 1- %3D dx

A: Apologies. We only answer one question at a time. We will answer question 1 as the exact one wasn't…

Q: -= 3x+y², Use the Modified Euler's method to find y(0.1) correct to 3 decimal places given dx…

A: Modified Euler's method uses the formula: ym+1=ym+hf(xm+12h,ym+12hf(xm,ym)) to perform the…

Q: Solve the equation dy/dx=1-y , given y(0)=0 using modified Euler’s method and find y at x=0.1 and…

A: Given differential equation is, dydx=1-y, y(0)=0. To find the solve the differential equation using…

Q: 2. Variable Separable eyx a) dy =D dx ey+x?ey

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Q: Zy dx = (x?-1)L dx-dy) %3D

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Q: Solve for the general solution of the given DE by using the integrating factors found by inspection.…

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Q: Given: (1 + 2x)e*dx Using integration by parts and letting u = -1 - 2x, dv = f (x) dx then the value…

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

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Q: f y=y(x) is the desired solution of 2 = f(x,y), Derive Euler %3D teration formula for solving ODES…

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Q: Solve four questions of the following DEs 1- xy dy + (x? + y? )dy = 0 dx 2- 2 - y = e*/2 dy 3- (x +…

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Q: 6) 3x²y dx + (x² + y²) dy = 0 3

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Q: Step 3 The total differential dz for the function z = x?y is dz = ydx + dy.

A: We need to find dz.

Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y (0) = 3

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Q: Of Find the general solution for the following first order D.Es? (Answer two only) sinx+cosh 2y-…

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Q: 1) Find the solution of the following equation: y"+ ly 0, with y (0) = 3 and'y (0) = 3 with A<0. Is…

A: Let λ=-a2&lt;0 Then, y"+λy=0 ⇒y"-a2y=0 Auxiliary equation is m2-a2=0 ⇒m=±a So, the general solution…

Q: (a) Find the differential dy. y = e/3 dy = (b) Evaluate dy for the given values of x and dx. x = 0,…

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Q: Given dy = yx + e*y, y(0) = 1, h = 0.5 dx By using Euler's method, the value of y(0.5) is most…

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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: Q11. For the ODE dy = (y cos (x) + 2x)/y ,y(0) = 0.8 dx The most accurate answer when estimating…

A: (a) Third order R-K method:- k1=hfx0,y0 k2=hfx0+h2,y0+k12 k3=hfx0+h,y0+2k2-k1 y1=y0+16k1+4k2+k3 (b)…

Q: When reduced to a linear DE of order one in z, the Bernoulli's equation dy +y dx = 3x?y? becomes dz…

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Q: Find the specific solution for the following ODE: dy = 2y dx Knowing that y ( 0) = 3

A: We can solve the given differential equation by using initial condition.

Q: 3 y = √√2x + 7

A: Given,  y=2x+73 or x=y3-72

Q: 2. Use Runge-Kutta method to solve the IVP dy x +y? y(1) = 2. dx ху Use h=0.2 and approximate y(2).…

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Q: Given dy =x +y with y(0) = 1 %3D dx Determine the value of y when x = 0.1, with step size h = 0.05…

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Q: (2y² + 3x) dx + (2xy) dy = 0 .

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Q: Given the DE: (5x - y)dy + (3x - 7y)dx = 0 Show your solution clearly and completely that the above…

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Q: Find the differential dy and (b) evaluate dy for the given values of x and dx. y=ex/10 , x = 0, dx…

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Q: Solve the DE by Integrating Factors 1. y² dx + ( 3xy + y² - 1) dy = 0

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Q: In the given DE, cos x + In y + ( + ev = 0, integrating the coefficient of dx, M (x, y), with…

A: We will find the g(y) as shown below

Q: Find an integrating factor for the linear DE of order one dx + (2xy – 1)dy = 0. (1)y? (2) ey² (3) x²…

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