If = ky and k is a non-zero constant, then a possible solution is ekt, a + 3 O (E) O kt + 5 O 2eky

Q: In Bernoulli equation y' - xy = xy³, the value of 1(x) is ex² False True O

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Q: Solve the given DE y'= X - x 3 — 2y 3 3ху 2

A: We have to solve the differential equation

Q: Find an explicit form of the general solution of the following ODE: (x – 1) y" + 2y' = 0.

A: Given

Q: Suppose a metal cube is heated to temperature 100 ° C uniformly through the cube, and then placed in…

A: Newton's law of cooling

Q: Q.4 Solve Cauchy Euler DE x³y" + 4x²y" – 5xy' – 15y = x*

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Q: Find the general solution of the following ODE. y" – 2y' + y = e* x=²

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Q: Let y(x) be the solution for the DE : y = (x + y + 2)2 If y(0) = -2, then find y() ○2-푸 O 8 - T O -…

A:

Q: A. ELIMINATE THE ARBITRARY CONSTANT/S IN THE EQUATION. 1. y= Ae2x + Bxe2x 2. y = Ax² + Be¬* 3. y =…

A: Explanation of the answer is as follows

Q: Solve the initial-value problem x' = Bx, x(0) = xI for the following B and xI.

A: Part A)- Given: Given matrix B=-2-11-4,x'=30 We want to find solution of x'=Bx Solution: We want to…

Q: d the general solution of the following first order x = 5x1 – 6x2 + 3e2t x2 = 3x1 – 4x2+e²

A: Rewrite given equation as (D-5)x1+6x2 =3e2t              ...(1) 3x1+ (D+4)x2 =et…

Q: 2 100 Given A = |4 3 6 x = and b = | 350 L0 -1 200 Solve the maxtrix equation Ax = b for x

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Q: 1. 3(3x² + y²)dx – 2xydy = 0 -

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Q: Solve the following using variable separable. (y’)2 =  1 − y2/1 − x2         ;         y = 1/2, x…

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Q: 8. Solve the following LP algebraically. a. Max Z= 150X+ 160Y subject to: X+Y 20 Y>15 X, Y>0

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Q: solve the given initial-value proble x1'=2x1+x2, x2'=-x1+4x2, x1(0)=1, x2(0)=3

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Q: If x1=2, Xn=4X(n=1)–4n Vn22. Find the general term xn

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Q: Let y(x) be the solution for the DE: y (x + y +2)² If y(0) = -2, then find y() 7- 3 4 2+ O 8 JTO 3…

A:

Q: If y1=x2+x°is a solution for x²y"-4xy'+6y=0, then the second solution is Select one: a. -In(x+1) O…

A: we have to solve given problem:

Q: 2. xty'= -x³y- csc(xy)

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Q: The general solution of the DE: y = 1 is y = x(x + c) Select one: O True O False

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Q: Solve for x. In(5x – 3) = 2 O x = e2-3 O x = 1 e-3 a = e+3 O x =

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Q: Solve e = 1 + V3i for all values of z

A: Given,              ez=1+3i

Q: 3. Derive the reductive formula for S sec" (x) dx.

A: We will find out the required solution.

Q: dy )=ax+ by, where a and b are non-zero constants, is dr The general solution to the DE n O In…

A:

Q: Solve the following homogeneous ODE 3. y' = 2ху y² –x²

A: Given: dydx=2xyy2-x2...1 Let, y=vxSo,dydx=v+xdvdx

Q: y = 3 (y + 1)

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Q: e 2t * – 3x + 2x = e2t+1

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Q: If e-x, xe-x are the solutions of y''+ay'+by=0 then, what are the values of a and b.

A: To find- If e-x, xe-x are the solutions of y'' + ay' + by = 0 then, what are the values of a and b.

Q: 4.) Give the general solution of the following ODE: x" + 3x - 4x = 0.

A: Given is the ODE x''+3x'-4x=0 The objective is to find the general solution.

Q: Solve the following D-E 2) x- 2y = x³cos4x dx

A: Topic- solution of linear differential equations

Q: Find the general solution of the given DE 2xy^2 + 4 = 2(3-x^2y)y'

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Q: 5. Find the largest constantr so that o(x) = e"¤ is a solution to %3| y" – 2y" – y' + 2y = 0. -5 1 O…

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Q: Find the general solution of the DE below. y(1) + y “ + y“ = 0 יינ

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Q: Find the general solution of the following DE. y' = 3 (y + 1)

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Q: 5. Find the particular solution of x²y' – 2xy = x* + 3; where y = 2 and x = 1

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

Q: Solve e = 1+ V3i for all values of z

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Q: S'z xdx (1+x)*

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Q: Find the general solution of the following DE. xy² (y')² + y(x - 1)y' - x³ = 0

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Q: 4. Find the constant a so that e +y = I-l is an implicit solution to e %3D tay O 5/2 О 32

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Q: Solve CO (z-2)² 3ln 2-2-¹³ +C In | x − 2 − ₂ + C None of the Above 2 ln | x − 2 + + C

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Q: 1. Find an interval for which the following has an unique solution: (x-2)y"+3y = x, y(3) =2,y'(3) =…

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Q: The form of the exact solution to 2 + 3y = e, where y(0)=5, is O 5e -1.5z + xe- O 5el.5 + e- O None…

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Q: Find the general solution of the following ODE: y''' − y''− y'+ y = 0.

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Q: 5. Find the particular solution of x²y' – 2xy = x* + 3; where y 2 and x = 1

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Q: Eliminate the arbitrary constants of the following. General solution 1. y = cx + c? + 1

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Q: Solve the given O.D.E. by the method of "Variation of Parameters"; 1 Y" - 4 Y' + 4 Y = [12 x2 -…

A: The solution is given as

Q: 5. Find the largest constant r so that o(x) = e"" is a solution to y"-2y"-y+ 2y = 0. -5 O 2 O 7/2

A: