Which of the following equations is variable separable? a. (x2 + y?)dx – xydy = 0 O b. (3x? – y?)dx – 2xydy = 0 O c. dy dz y?+2zy O d. r(y + 1)?dx + (x²ye + ye)dy = 0

Q: Determine the particular solution. (2xy)dx = (y² – x²)dy × = 1, y = -2 2 = 3x3y + y3 O 3 = 3x?y + y3…

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Q: Find the general solutione (3xy — 4y3 + б)ӑх + (x? — бх*у? — 1) dy %3D0 а. (х +у-2)? %3D с (х — у +…

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Q: Let us solve the following equation via separation of variables J²u(x, t) Ət² = 7 d²u(x, t) ?х2 a)…

A: The given equation is ∂2u(x,t)∂t2=7∂2u(x,t)∂x2. Solve the equation by using separation of variables.…

Q: Which of the following equations is variable separable? O a. dy y²+2zy zp O b. r(y+ 1)²dx + (r²ye" +…

A: We need to choose the differential equation which is variable separable. A differential equation is…

Q: Which of the following is a solution to xy' + y + x*y*e* = 0 ? y3 = x³(3e* + x) y3 = x³(3e* + C) %3D…

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Q: Which of the following is a solution to xy" + y' = 0 ? y = = 1 y = x3-x O A y = In x %| O D В

A: A function y = f(x) is said to be solution of the given equation  xy" + y' = 0  ...(1) if  y = f(x)…

Q: Q4/ B/ If Ø = (x³y²z) and A = 2xz i - 3y²j+ 3xy²k Find 0(ФА) ay əx the point (2, -1, 3)? at

A: Given: ∅=x3y2z and A→=2xzi→-3y2j→+3xy2k→  To find: ∂∅A∂y∂xat the point 2, -1, 3 To solve the problem…

Q: Use undetermined coefficients to find the particular solution to y''+ 8y' + 15Y = e 2"(13 + 12x) (13…

A: Consider y''+8y'+15y=e-2x(13+12x) To find the particular solution using method of undetermined…

Q: 5. Which of the following equations is not a variable separable? dy dy ry + 3x - y - 3 ry – 2x + 4y…

A: To write the equations which are not a variable separable differential equation.

Q: Which of the following equations is/are exact? b 32 ydx + (2a'y+ 4y) dy = 0 %3D O (ry + 1) dr + (ry-…

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Q: Determine for which values of m the function (x)=x" is a solution to the given equation. 2d²y dy (a)…

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Q: Let y1, Y2 be two independent solutions of (t – 1)y" – ty' + y = 0. If W (y1, Y2)(2) = e² , then…

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Q: Solve for the general solution : xydx – (x² + 2y²)dy = 0 Select the correct response: 2*y = 4y°…

A: The given differential equation is: xy dx-x2+2y2 dy=0

Q: Which of the following equations are separable? adß+ Bda + aßB(3da+dB)3D0 ( +1)y'= y 2x IL IIL…

A: A differential equation is said to be separable if the variables can be separated. That is, a…

Q: dy x*y3 = X dx and y(0) = 2.

A: find the solution of the given differential equation

Q: Find the solution set of the linear equation(s) in the following A. 2x- y² = 10 В. y =1 C. ex-y =5…

A: A. as degree is 2 . it is not linear equation.   B. as degree is 1 . it is linear equation.   C. as…

Q: Find all values of the constant c so that (xy + 1)dydx = 4 + 4c. 1J0

A: An iterated integral is an integral over several variables where each variable is integrated over…

Q: Obtain the general solution.  1. (D4 + 3D3 + 2D2) y=0  when x=0, y=0, y'=4, y"=-6, y'''=14 2. (D3…

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Q: 9. What is the solution of (x? + 2xy – 4y² )dx – (x² – 8xy – 4y² )dy =0 ? a. x? - 4y? = c(x-y) b. x?…

A: This is homogeneous differential equation. For solving this we will assume,  Y/X = V dy/dx = v -…

Q: Find two values of r such that y =x" is a solution of x*y" + 4xy' - 18y = 0 , x> 0. O A. r= -9, 2 O…

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Q: Find the general solution of (ye – 2y³) dx+ (xe А. еxу + 2хy3 - у? %3D С В. е — 2ху3 - у? %3D с 6xy2…

A: We have to solve the problem

Q: The solution of the following IVP:y'=y³ x e*, y(0) = 1 Select one: O a. y=V4-2 ex2 O b. 1 V2- ex? C.…

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Q: Solve the following diffential eauations a) dy + 4 y = e dy 3n2y = そ? ea3 dy C) N + 2y = そマ dn

A: We need to solve DE.

Q: Solve by variable separable. 4.)(4y + yx³)dy – (2x + xy*)dx = 0 5.)2y(x +1)dy = xdx NOTE: Only the…

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Q: 3. Find the general solution of 2xydx + y?dy = 0 A. y? = 2(c + x2) B. y = 2(c - x2) C. -y? = 2(c +…

A: This question is based on solution of differential equation.

Q: Which of the following equations is not a variable separable? dy dy ту + 3х — у — 3 (a) e30+2y (b)…

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Q: 7. Find the general solution of the following DE. a. (D2 – D- 2)y = 0. b. (D2 + 3D)y = 0. c. (D? – D…

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Q: 5. Find the general solution of (6x - 7y) dx - 14xy dy = 0 A. x(2x? + 7y²) = C B. y(2x? + 7y2) = C…

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Q: Which of the following equations can be reduced to be a separable equation? 1. (2гу — tan y)da + (ӕ?…

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Q: Which of the following equations can be rearranged into separable equations? O y – y? = t - O y +…

A: y' + yt² = t² can be written as separable equation as : y' = t² - yt²  So, y' = t²(1-y) So, dy/(1-y)…

Q: Which of the following equations is not a variable separable? ту + 3х — у — 3 ry – 2x + 4y - 8 dy dy…

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Q: Which of the following equations is variable separable? O a. (3a2 – y²)dx – 2aydy = 0 O b. (z² +…

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Q: Find two values of r such that y =x' is a solution of x*y" + 4xy' - 18y = 0, x> 0. O A. r= -6, -3 O…

A: Given differential equation is a linear, homogenous differential equation with variable…

Q: Which of the following is not a solution to d'y dr? 4y +1 -2z O y = e2 + e O y = e2 . -2x e - 1 O y=…

A: we have to solve

Q: 9. Which of the following equations are separable? Write those that are separable in the form y' =…

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Q: — хz + 2ху %3 0. xy ay az az Solve, y? ax

A: Lagrange's Method: Let us consider a standard form of the first order partial differential equation…

Q: Which of the following equations is variable separable? O a. (x² + y²)dx – xydy = 0 O b. dy dz…

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Q: 5. Which of the following equations is not a variable separable? dy (a) y – 3 xy – 2x + 4y – 8 dy XY…

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Q: C. Find for the general solution of the following DE. 8. (D3 + 3D2 – 4D)y = 0 9. (DA + 6D3 + 9D²)y =…

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Q: Which of the following equations is variable separable? dy O a. dz y²+2xy O b. (3x? – y²)dæ – 2xydy…

A: A separable differential equation can be written as dydx=fxgy. A first order Bernoulli ordinary…

Q: Which of the following equations can be reduced to be a separable equation? 1. y +y?dx - x(x + Va2…

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Q: Which of the following equations can be reduced to be a separable equation? 1. (x – y ln y + y ln…

A: Given : I. x-ylny+ylnxdx+xlny-lnxdy=0II. ydx=x+y2-x2dyIII. 2x+3y+1dx+-2x-3xdy=0 To find :…

Q: 9. What is the solution of (x? +2xy – 4y? )dx - (x² – 8xy – 4y² )dy =0 ? a. x? - 4y? = c(x-y) b. x?…

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Q: Find the general solution by substitution or elimination Q6 A: = x -2 y +t di =x- y +2t *= -y +…

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Q: Which of the following equations is variable separable? dy y?+ 2zy O a. dz O b. (3a? – y?)dx – 2xydy…

A: To find which of the given equation is variable separable. Q

Q: Which of the following is the general solution of the separable equation, dy/dx = 12x³y? A. y =…

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Q: The solution of the following IVP:y' =y³ x ex, , v(0) = 1 Select one: O a. V4-2 ex2 b. V =V2- ex² C.…

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