Find the general solution using substitution of each of the following DE: 1.) (2x + y + 6) dx + (2x + y) dy = 0

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Q: Solve the Cauchy euler equation d³y x3 dx3 3x2 d?y dx2 2 + 6x -6y = 3 + Inx³ dy dx

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Q: Find the general solution of each of the following DE: A. Substitution 1. (2x+ y+ 6)dx + (2x + y)dy…

A: Hi! Please find the answer for the first question. According to the protocol only the first one can…

Q: The solution interval of 2y +12≥3 or 3y 1 or y≤ -1} .B O (-∞, -1]U (1, ∞ ).CO {yly ≥1 or y<-1} DO

A: We have to find the solution interval of  2y + 1 ≥ 3 or 3y &lt; -3

Q: At the point (3, -1, 2), * P = xy + yz + zx A = x²yî + y²zĵ + z²xk Find p · VA O 1 O 2 O 3 O 4

A: As per our guidelines we need to solve only one question. Please repost the remaining questions as…

Q: Find the solution to the IVP.y = cscx – ycotx' y(÷)= 1 ysinx = x+ 2 ysinx = x + 1- I 2 ycscx = x +…

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Q: Q14- Solve the equations to find x, y, z by Gaussian elimination : 3 x+z = 4 2 -3 x+3y - 2 5 X - 5 =…

A: Given: The given system of equation is,

Q: 4. Find an implicit solution using the substitution u= or y3ux dy dx x+xy %3D

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Q: Which of the following is the particular solution to the DE y(9x-2y)dx- x(6x-y)dy 0; y(1) 1? A.…

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Q: after solving for the factors of dy/dx, the equation y*[(dy/dz)^2] + 2xdy/dx - y = 0 will reduce…

A: Answer is option (d) homogeneous  Just make it in the form of ax^2+bx+c =0  By assuming t= dy/dx…

Q: find the solution to the Cauchy-Euler equation on the interval (0,∞). In each case,m and k are…

A: Since we have to find the Cauchy-Euler equation, we will substitute y=xm which will yield…

Q: Find the General solution Use method of undetermined coefficients. 1. (D² l)y=ex (2sinx + 4cosx).…

A: To Find: the general solution using the method of undetermined coefficients   1. D2-1y=e-x2 sin(x)+4…

Q: Use variation of parameters to find a particular solution of the DE y/" – 4y + 4y then write down…

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Q: The general solution of the following Euler Cauchy equation: d²y x². dx2 + 5x = -3y y(1) = 2, y'(1)…

A: We have to solve the Euler's Cauchy equation

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Q: 3. Find the general solutions of, (xy + x* )dy + y°dx = 0 b.

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Q: Which of the following is the general solution to the DE (2x-y)dx+ (4x +y-6)dy 0? A. (x+2y+1)…

A: We have to solve given differential equation: given DE is(2x-y)dx+(4x+y-6)dy=0 ---(1)we can write…

Q: Solve the following Euler-Cauchy type equation: 1 (x² D² + 3xD+ 1)y = - 3xD+ 1)y = (1 – x)² ' d…

A: Given equation is, x2D2+3xD+1y=1(1-x)2 Take, (x2D2+3xD+1)y=0 Then assume, y=xn,…

Q: 1. (3x – 2y + 1) dx + (3x- 2y +3) dy = 0, %3D Ans. 5(x + y+ c) = 2 In | 15x - 10y + 11L

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Q: Obtain the family of solutions 1) xydx – (x² +3y² ) dy = 0 2

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Q: Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a have a…

A: Given: Find the relation between a, b, c and d for which the equations ax + by = c and cx +dy = a…

Q: Find the Particular solution of the ODE d?y dy -6--7y = -9e-2x, dx2 at y(0) = -2 and y(0) = -13 %3D…

A: We have to find the particular solution of the ODE                       d2ydx2-6dydx-7y=-9e-2x at…

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Q: 1. Solve for the othogonal trasctories y =x²(1-cx)

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Q: first finding particular intergral and complimentary solution.

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Q: 1. Find the general solution. а. (3х — 2у + 1) dx + (3x — 2у + 3) dy — 0 Ь. dy/dx 3D (9х + 4у + 1)?…

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Q: (b) Solve and by applying chain rule if z = In(x² – 2y), and x = : az u + v, y = e".

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Q: Find the general solution of the given ODE: dy x²y-4y dx x+2

A: The solution of the given differential equation is  y=e(x22-2x+C)or y=Ce(x22-2x)

Q: Solve the Cauchy euler equation d²y + 6x 2-6y = 3 + Inx3 dx x3 d3y 3x2 dx2 dy dx3

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Q: dy + ydx %3D = 3x²y?dx,

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Q: 3. Find the general solutions of, dy _ x+ y dx х-у, a.

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Q: Use undetermined coefficients to find the particular solution to y''−9y'+20y=−1768sin(t)

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Q: Solve the Cauchy-Euler equation: x*y' Зху + 4y = 0. %3D

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Q: Show that the homogenous equation (Ax + By) ⅆx + (Cx + Dy) ⅆy = 0 Is exact if and only if B = C.…

A: Please refer the attached image for complete solution.

Q: 3- Use Euler Method to find value of Y(1.6) when Y(1) = 0 for %3D (x2 + y2)dx = (x + y)dy, use h =…

A: The solution is given as

Q: Find two values of n such that y = enI is a solution of y" + y' – 72y = 0

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Q: 3. Find the general solutions of, dy_x+y dx х-у, а.

A: given differential equation is  dydx=x+yx-y

Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D. Answer:

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Q: Find the general solution of the given DE (x-3y-1)dx-(x-3y+5)dy%3D0. Answer:

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Q: What are thr genereal solutions of the following? a) y^2 dx + (x^2 + 3xy + 4y^2)dy=0

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Q: A second order Caushy - Euler equation having a solution y(x) = x=²cos(3Inx) is Ox²y" +5xy' + 4y = 0…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.