Solve the ordinary differential equation 6x2y” + 6xy’ = 294y - 6x2y . Then evaluate the first four terms of the particular solution at x = 5.416. Round off the final answer to five decimal places.

Q: solve the differential equation using variation of parameters: 2x2y′′ + 5xy′ + 9y = -x2 - 2x. only…

A: The given problem is to find the solution for the given differential equation by using the variation…

Q: 2. Show that if a > 0, then the sequence (²x²e¬n) converges uniformly on the interval [a, ∞), but…

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Q: Solve the differential equation: y = 3x +log P.

A: Given equation is y=3x+log P Let us consider P as a constant and then dydx=ddx(3x + log…

Q: dy dx 2₁ y x = x + 2√/ X X

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Q: 11. (2х — бу + 4)dx + (х — 2у — 3)dy — 0; when x — 1, у %3 1

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Q: an² y dx = sec²x dy

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Q: Solve the differential equation  4yp2-2px-y=0

A: Given: The differential equation, 4yp2-2px-y=0   To solve: The given differential equation.

Q: When a transistor radio is switched off the current I (in milliseconds) falls away according to the…

A: The differential equation governing the current I in the transistor radio is given by: dI/dt = -0.4I…

Q: Solve the following differential equations: 1. y(lnx - In y) dx = (x ln x - x ln y - y) dy

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Q: 13.ydx + (3x —ху+ 2)dy — 0

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Q: 12. (4х + Зу — 7)dx + (3х — 7у + 4)dy %3D 0; whe х %3D 1,у %3D1

A: Solve for the differential equation (4x+3y-7) dx + (3x-7y+4)dy=0; when x=1,y=1.

Q: 9. (x + x* + 2x²y² + y4)dx +y dy = 0; when x = 1,y = 1

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Q: - (t/z? + y² – y) at dt + (y/t² – y² – t) dy = 0; when t 3,y = 4

A: Answer is  ty=3(t2+y2)3/2-363

Q: 10. (2ху*eУ + 2хуз + у) dх + (x?y*eУ — х?у?— 3х) dy — 0; when x - -1, у — 1

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Q: (xy + y ln y)dx + (xy + x In x)dy = 0; when x = 1, y = 1

A: 7. The given differential equation is  (xy + y ln(y))  dx + (xy + x ln(x )) dy= 0   ....(1) with…

Q: 6. (y cos x + 2xev)dx + (sin x + x²e° + 2)dy = 0; when x = 0, y = 0

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Q: 3. у(3x3 — х + у)dx + x?(1 — х?)dy 3D 0 4. у(2х — у + 1)dx + x(3х — 4у + 3)dy 3D 0 5. (r + sin 0 –…

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Q: y = Cje² + C2xe* + C3x²e* %D O y" + 3y" + 3y' + y = 0 y" – 3y" + 3y' + y = 0 %3D + 3y" + 3y' – y = 0…

A: Given data is: y=C1ex+C2xex+C3x2ex

Q: 4. cos x dy + y(sin x – 1)dx = 0; when x = T, y = -2

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Q: Find the Differential Equation: xInxdy + xydx = Inxdx

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Q: 5. (e* – sin y)dx + cos y dy = 0; when x 0,y = 1/2

A: First we will convert the given differential equation into linear differential equation by…