(1 – a*)y/" – - 2.ry' + 2y = 0.

Q: (3y²-x²» = 0 ;when x = 1, y = 1 2y4

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Q: au au = xt at (x > 0,t > 0) ax u(0, t) = 0 u(x,0) = 0

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Q: xY + x) dy + ydx = C = xy – 3y³ C = 3xy + y° О Option 1 Option 2 C = xy – 3y3 C = -3xy+ y

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Q: y" +9y' = 9 tan 3x

A: The solution is given by using method of variation of parameters as follows

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: (2xy + x)dy – [x² + y² + y + 1]dx = 0 When:x = 1; y = 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: dy dx = x+1 2(y+3)

A: The given differential equation is dydx=-x+12y+3. Solve the given differential equation. Here we use…

Q: Solve the differential equation using the power series method.

A: Given a differential equation,                                              x+1 y' - 2x+3 y = 0 . We…

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: Solve [æ – y cot ( ) dæ + x cot () dy = 0 ; y (5) = 1

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Q: (x² + 2xy- 4y?)dx- (x² – 8xy– 4y²)dy=0 | O x² + 4y² = C(x + y) O x2 +y2 = C(x+ 4y) O x2 + 2y? = C(x…

A: Solution(x2+2xy-4y2)dx-(x2-8xy-4y2)dy=0dydx=x2+2xy-4y2x2-8xy-4y2(∙)this differential equation is…

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: Solve the differential equation. Indicate the type of differential equation

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Q: y" - xy = 0 2) Solve for term of X7 . Final answer must Show the series until

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Q: 2. 2x sin? ydx – (x² – 9)cos ydy = 0 -

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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…

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.