Which of the following equations is variable separable? dy O a. dz y²+2xy O b. (3x? – y²)dæ – 2xydy = 0 O c. #(y+1)²d + (x²ye" + yev)dy = 0 O d. (x² + y² )dx – xydy = 0

Q: Solve the pollowing: り ( 2+J(xtjy) X=? ye! (b) (2+j)(3-j2) = a+jb a:? b:? (C) (メ-j2y) -(y-jx)-2j x=?…

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Q: For the equation Mdx+Ndy=0, if both M and N follows that f(Ax,\y)=^k f(x,y), the equation is A.…

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Q: (a) 2+j - j(x+jy) メ=? y-? 1-j (b) (2+j)(3-j2) = a+jb a=? be? ((メ-j2y) -(y-Jx)-2) x? y?

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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: (x² + 4xy + 2y²)dy + xydx = 0

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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: 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: Which of the following equations can be reduced to be a separable equation? 1. (22 + ry? - y)dr +…

A: We will check whether we can reduce the given differential equations in variable separable form

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: Q1.Find the general solution of following PDE equation (a) (5z+ R)uz + (7x+ R)u, R (b) (z + R)u, +…

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Q: Which of the following equations can be reduced to be a separable equation? I. (z- y ln y + y In…

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Q: Find the particular solution to D²y – 6Dy + 9y = e3x – ex when x = 0, y =y' = - 3 %3D

A: For given differential equation we have to find particular solution.

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: Obtain the particular solution 1. (D³ +6D² + 12D + 8)y=0 when x = 0, y = 1, y'= -2, y" = 2 2. y" +…

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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: Solve the following equation by using separation variable method: y(x,0)=10 1>0 0<r<A y.(0,1)= y,…

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Q: Let y1, Y2 be two independent solutions of t?y" – 2y' + (t + 3)y = 0. %3D If w(y1, y2)(2) = 3, then…

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Q: Obtain the GS of: 2 (Згу — 4у + 6) dz + (23 — ва? ? — 1) dy %3D 0 - a. x³y – 2x?y3 + 3x² b. x3у —…

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Q: Solve the IVP y" – y + 0.25y = 0 with y(0) = 2, y' (0) = 1/3 y(t) = 2e/2 – ?et/2 - O _ 꼭et/2 y(t) =…

A: Given y"-y'+0.25y=0 with y(0)=2 , y'(0)=13

Q: Let a ∈ R and find the solution to y'(t) - a y(t) = 0.

A: The given differential equation is dydt-ay=0 , a∈R.we will slove this by the method of  separartion…

Q: Ex: FIND A COMPLETE SOLUTION OF EQ. y" + 3y" + 3y' + y = 0

A: The given differential equation is y'''+3y''+3y'+y=0. Find the complete solution of the differential…

Q: Which of the following equations is the DE whose solution correspond to y = C1sin3x + C2cos3x + 9x²…

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Q: Find two values of r such that y =x' is a solution of xy" - 4xy' - 24y = 0 , x> 0.

A: Given:                 x2y''-4xy'-24y=0y=xr Differentiating y=xr, we get…

Q: :-Solve the following equations (choose three only):- 2 1- y' + ²y = -x³y5 2- 2xydx + (x²-1)dy = 0…

A: As per the guidelines I am supposed to do the first question among multiple questions. So here I am…

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: Which of the following equations can be reduced to be a separable equation? 1. (2ry - tan y)dr + (x2…

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Q: Rewrite the following equation with the variables separated. 3√t + y² dy = 6 dt o y² dy = (6 + 3√t)…

A: Please see the below picture for detailed solution.

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: 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 is variable separable? a. (x2 + y?)dx – xydy = 0 O b. (3x? – y?)dx…

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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 is the general solution to the equation (2x+9)y" +(2x+7)y-2Y3D0? O a. y=c_1…

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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/are exact? O (ry + 1) dr + (ry – 1) dy = 0 3x y?dz + (2r'y+ 4y°)…

A: To check the exactness of the given differential equations. As per the policy only solutions for…

Q: Which of the following equations is variable separable? O a. (3x2 – y?)dx – 2xydy = 0 O b. (2² +…

A: An equation is called variable separable if we can separate the variables x and 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: 9. Which of the following equations are separable? Write those that are separable in the form y' =…

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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: Which of the following below is NOT an ordered pair solution to f(x) = Vx+7 O (-7,y) O (-8.y) O…

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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: 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: dy. Find the particular solution: t 2y 2t, y(-2) = 4 %3D %3D

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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: Solve the following DE: (2xy + 3x²) dæ + (2xy+ 4y) dy = 0 O a²y? + x³ + 2x?y? + 4y3 - 2xy = C O a'y?…

A: Solving the given differential equation

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

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Q: Find the solution to I' : y' 10z + 3y %3D if z(0) = 0 and y(0) = 9. z(t) = help (formulas) y(t) =…

A: We have to find all eigenvalues and corresponding eigenvectors for the coefficient matrix of the…

Roots

The main dissimilarity between real and complex roots is that the real roots are obtained as real numbers, in contrast with the complex roots, which are indicated as imaginary numbers. The standard format for depicting any complex number is in the form of a + bi.