Find the solution of the following initial value problem d2y/dx2 + 2 dy/dx − 3y = 12ex ,  y = 0 and dy/dx = 0 at x = 0.

Q: Suppose that x and y represent the amounts of two basic inputs for a production process and…

A: Suppose that x and y represent the amounts of two basic inputs for a production process   The…

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A: solve the differential equation by separating the variable and integrate it.

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A: (6) Given differential equation is y−4x−12dx=dy....1 We have to find the solution of the given…

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A: In this question,  we solve given DE by substitution methode i. e.  We put some terms in the form of…

Q: The Bernoulli's Equation dy/dx - y[1/(2x)] - y^5 = O can be transformed in which of the following…

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Q: Find d2y/dx2 if x = 3 - 2z and y = z2 - 3z3

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Q: Find d2y/dx2 for the equation x=x3y2-3y3

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Q: 1. Solve: 2 dy (2y + 3) dx 4x + 5,

A: The answer of the differential equation is, 2/(2y+3) = 1/(4x+5) + c, where c is an arbitrary…

Q: Solve (3x*y? – x²)dy + (4x³y3 - 2xy)dx 0 %3D | | .3

A: Given differential equation is exact differential equation. We solve it as follows:

Q: Find the solution. (dy/dx) + xy = xy³ A x = (ce-²-1) By = (ce²+1) 7² y = (ce x²-1) x = (ce)² + 1) ²…

A: We have given a differential equation ,  dydx + xy = xy3 Multiply throughout by dx ,  dy + xy dx =…

Q: If dy/dx = 4x/y and y(0) = 5, find an equation for y in terms of x. A x²/2=2y² + 25/2 B. y²/2 =…

A: To solve the following problem

Q: 1. Find the solution of +=3x ; y(2)=3. dx 4x

A: we have to find the solution dydx+y4x=3x ;  y(2)=3

Q: 1) S(1– x)V dx. 2) Sxsec²(4x² – 5) dx.

A: detailed solution is given below

Q: dy 1. Determine the general solution of x = 2 – 4x3

A: since u have asked multiple question in a single request so we will be answering only first…

Q: b) Solve (D 3D + 2)y= x + sin x where D

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Q: Obtain the particular solution when x = -1 and y = 0 1 (2x + 3)dy = ydx + (2x + 3) dx

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Q: 1. y = x3 – 2x² + 3x – 5 - - dy 3x2 – 4x + 3 - dx

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