А. Classify the following differential equations according to order, degree and type Differential Equation Order Degree Туре 1. X - yy' = 0 a2 2. y" = y3 dh + 2h = 0 dr 3. d?y k’y 4. dx2 a2u 5. ( %3D du + = 0 ду d's 6. ( dt3 3ds = 0 t2

Q: 7. y - y = 16

A: The objective is to find the general solution .

Q: Find the solution. y'+=V5.y(1) = 0

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Q: 2хy -y' y2-x2 a. 3yx? + y3 = k Зух? — Зу3 c. 3yx? - y3 =k d. yx? – y = k e. Not in the list. b. %3D…

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Q: Which function satisfies the differential equation.  5. 2y - xy1 = 0

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Q: Calculate each of the given differential equation using Integration Factor found by Inspection 5.…

A: Explanation of the solution is given below...

Q: 4 j³g du³ + use Here equation. J J du² Sympy dy jn - y = o solve the differential

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Q: Solve the differential equation (D² - 5D+4)y = (7x + e*}.

A: As you post multiple question, I only solve first one. D2-5D+4y=7x+e-x2 Auxiliary Equation:…

Q: 9. (3x – y + 6)dx + (6x – 2y – 6)dy = 0 hint: Case 1 %3D

A: Given

Q: Match the differential equation with its direction field. y' = 8(x + y) - 1 I -Q.31 +0,2 -0.1 0.1…

A: To find- Match the differential equation with its direction field. y' = 8x + y - 1 Give reasons for…

Q: Solve. 4x²y" +y=0 1. xy" – y' =0 2.

A: differential equations

Q: Choose the correct answer If x2 + y2 = 9, then y'=...  -y/x  y/x  -x/y  x/y

A: We have to find y'

Q: 4. sinx-siny dy + cos x-cosy dy The ㅠ X = 6 = T|Y प = 0

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Q: The integrating factor that transforms the differential equation 3y" – 6y' + Axy = 0 , into a…

A: The differential equation of the form, A(x)d2ydx2+B(x)dydx+C(x)y=0 can be transformed into a…

Q: Find the general solution of the following differential equations: a. +6- dr + 9 0. dr3 dr² dy + 4.…

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Q: Determine the general solution of the differential equation: dy _Y -1+ x dx Select one: Оа. X. x² 2…

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Q: 4. dx -ydy - y² dx +xy dy =D X = 2 y=2

A: Compare this equation with,So here we have

Q: 8. (Зх — у — 1) dx + (9х — Зу + 4) dy %3D0

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Q: 3. 3xv'dx + (3x?y +y)dy = 0; Y(1) = ?

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Q: (ху + 1) dx + (ху — 1) dy %3D 0

A: As per the instruction, we will be answering only the first one. Here, M=xy+1 and N=xy-1. Now,…

Q: Solve the differential equation y' -2y =4-t Select one: 2t а. у%3-1.75 + се 2t b. y=-1.75 +0.5t + ce…

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Q: . (D² + *. + D)y = 6 + 3 e²

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Q: Determine the equation whose y'= Y/3x. 3x2 = y3 A 1 у? y= 3 x2 © x² = y3 1

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Q: (x3-x)² .3. 2 5. у 3 х+1

A: We’ll answer the 5th question since we answer only one question at a time. Please submit a new…

Q: y' + 3y = 8

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Q: 21. 22. (D' + D - 9D' – 13D² + 8D + 12)y 0. Ans. y Ce+cze

A: We will solve the given differential equation.Below find the solution in the image.

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.