3. Consider the differential equation y' = f(x,y) with initial condition y(xo) = Yo. Show that with x1 = xo +h (h > 0), the solution at a1 can be obtained within an error of O(h³) by the formula h Yı = Yo + 2 (20; Yo) + „f (xo + h, yo + hf (xo, Yo)) 2

Q: (x+2)y" - y - (x+3)y = 0,

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A: Consider the differential equation dydx=xy+3x−y−3xy−2x+4y−8 Hence,  dydx=xy+3x−y−3xy−2x+4y−8…

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Q: (x+2)y" - y' - (x + 3) y = 0,

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Q: Let y'= 2xy²; y = a. (-4,4),(-∞, -4] b. (-4,4) c. (-4,00),(-4,4),[4, ∞) d. (-4,00),(4,∞), e. (-∞,…

A: Given,  y'=2xy2 and y=24/(x2-16)

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A: We have to solve the initial value problem yy'+x=x2+y2 with the initial condition y2=-12. We have to…

Q: Q5) Determine the general solution of the simultaneous differential equations:

A: To solve this system of simultaneous differential equations, we can follow these steps:Write down…

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Q: y = - is one of the solutions to the non-homogeneous Cauchy-Euler equation 1 x²y" + xy' – y x + 1…

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Q: Find the general solution to the differential equation y' + xy = x/y2 Are there any solutions for…

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Q: у" — Зу" + Зу' — у %3D х — 4е* -

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

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Q: (x + 2)y" - y - (x + 3)y = 0,

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Q: (B) Find the general solution of x'y" + xy' -y=x²+1 given that y, = x is a solution of the…

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Q: ) Find the general solution of the DE y = (2+y')x+ (y')².

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Q: 7. The differential equation which has y = C1r + C2x as its general solution is: 4 (a) y" – -y'+ y =…

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Q: 5. Solve the following differential equation using the Method of Variation of Parameters -2x y" + 3y…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.