1. Solve the following differential equations. dy a) = (y - 1)(y + 2) sin x b) c) y' y d) y' = y² - 2y al dx dy dx = = y C11

Q: dy dy (1) = 4 Solve: x d'y Solve: X - 2x - 10y = 0. Where y (1) = 5, dx dx dx

A: Given, The given equation is a second Euler homogenous ODE has the form of  ,

Q: 3-(cos x)y' =yCv-1) sin x.

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Q: (3x² – 2xy+ y²) dx + (2xy – x² + sin y) dy = 0, y(12) = 0 - |

A: We have to find the required solution of…

Q: 4- Determine an expression for dy/dx. 3(y-2)3– x= 4x - 6.

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Q: 1. (x2 + y² + 1)dx + x(x-2y)dy = 0 (Non-exact Equation) Ans: x² - y² + xy - 1 = cx

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Q: What is the domain of the following function: f(x) - ○ (2,00) Or 2 O[-1,00) O [− 1, 2) U (2, o) O…

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Q: dy/dx + 2xy + xy = 0 Ans. 1/y3 = -;+ 1 + ce3x? 2

A: The given differential equation is  dy/dx + 2xy +xy4=0

Q: dw 4w A) Give the general solution of dx = x³. B) Solve y' + = y²x³.

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Q: Solve the DE sinx siny dx + cosx cosy dy = 0 by separation of variables. (A) cos y sin x =C sin y B…

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Q: y" + 3y² - 2 = e².sint (Variation of parameters)

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Q: Solve the following D.Es: 1. (x + 1) = x(y² + 1).

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

Q: Show that y sin x is a solution to xy" + (2 secx)y' + xy = 2. =

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Q: 7. (x² +x – y)dx + xdy = 0.

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Q: 4. (y- Vx² +y? )dx- xdy = 0 when x= 3, y=1 +X1

A: The solution are next step

Q: (1+ In xy) dx + (-)dy = 0

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