2) .. Use separation of variables to find the general solution.   dy dt − 12t3e−y = 0.

Q: 4. Homogeneous: Solve the equations (x – y) dx + (3x + y) dy = 0; when x = 3, y = -2

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Q: Find the solution. dy x2-y?=2xy dx -2 A -1 B y = C y = 2.

A: Given Differential equation is x2dydx - y2 = 2xy

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A: First we will write the given differential equation in form of linear differential equation then we…

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Q: Find general solution of " – y – 2y = e2t

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Q: 6. Find the solution of dy = (y² – y)x². dr

A: Definition used -          The solution of the variable separable differential equation-…

Q: dy Solve the initial value problem: + 2y = 6e¬x; y(0) = 8

A: Since the given differential equation is first order linear differential equation so we first find…

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Q: Find dt OA. ○ B. OC. O D. for y = (5t? - 4t)?. dt dy dt dy dt dy dt = 2 (5t² − 4t) + (10t − 4) =…

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Q: dy dr y(5) = 2. リーエ

A: To solve the given differential equation.

Q: dx —х +3у dt 13. Find the general solution dy -3x+5y dt ||

A: The objective is to find the general solution of system of differential equations…

Q: d²x dt² dx dx 4+5x = 10; when t=0, x=0, x=0. dt dt +4.

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Q: 2. Solve the following: dt x> 2 X-y t+

A: The formula for the substitution method for definite integrals is given by , where g'(x) and f(x)…

Q: Solve the DE. (x³ + xy²-y)dx + (y³ + x²y + x) dy = 0 O arctan(‡)=C − x y O arctan (=) = C - x² - y²…

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Q: Find an equilibrium solution df/dx = 2f − 6. a. f = 2 b. f = 3 c. f = 4 d. f = 5

A: Given Data: Differential Equation: df/dx = 2f − 6 The equilibrium solution is the point where the…

Q: dy Find the solution of the Bernoulli's equation x + 6y = 3xy4/3. dx 1 1 а. у b. y (x2+cx)3 (x+c)3 1…

A: We solve by Bernoulli's equation.

Q: Find the general solution of y" - 6y"=3 - cosx.

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Q: Determine whether or not the following equation is exact. If so, find the solution. 1. (2xy² + 2y)…

A: Since it's a multiple question. So as per our guidelines, we are supposed to solve only first…

Q: dy e, solve the IVP = 40 dt 5y y(0) = 10. - %3D 100-4t cag

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Q: + 4 oly +6y =0 dt dy +2 -6x=6

A: Introduction:Simultaneous equations are those in which the derivatives of two or more dependent…