dx 3x – 5y dx = 3x – y + 2z +t-1 dt dt (a) dy = 4x + 8y dt dy (b) 2x -z- 3t2 dt dz x+y+z+t? dt

Q: dx 8х — 9у dt dy = x + 2y x(0) = 2 y(0) = 1 - dt

A: The solution is given as

Q: x2y3-y=x+x2 find dy/dt

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Q: Solve the following initial value problems using Laplace Transforms:

A: We need to solve the given differential equations using Laplace transformation. For (a),

Q: d²y dy 4+ 5y = t dt dt2 dy y(0) = 0 (0) = 1 dt

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Q: 1-² dx dy dz se ³ 1 xyz 2-fff(x+y+z)dy dx dz TL 3-fff₂y sinz dx dy dz 6 -2

A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…

Q: e particular solution of the differential uation x^2 dx - (y+1) dy 0 if y(0)=1 2y^2+3y-6x^3+6= 0…

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Q: dx = 7x + y: dt x(0) = 2 dy - 8x + y: y(0) = 0 dt The solution is x(t) = [O and y(t) = |

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Q: 3 dx – dy = o; y(o) = 6 x² dx + y² dy = o; y(9) = -1 x dx + 2y dy = 0; y(1) = 2 4 cos 2u du – e5v dv…

A: As per our guidelines we are supposed to answer only 3 sub-parts of a question

Q: dx dy - 2x – 2y. a) dt -x, dt dx = x + 3y, dt dy dt 2.x. b) dx dy (c) 3x – 4y, 2x – y. - dt dt

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Q: 2) t (y-1) dt +y(t+1)dly=0 31 хчуу! -2y =. 41 yan- x lnn dy ==

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Q: dx 2 dt dy + y = 0 dt d x d'y +x — у%3D 5е 2t - the dy(0) = 0; dt dt2 dt2 equation system dx(0) x(0)…

A: Solve, as follows:

Q: dx? dy = y(t) - dt2 dt dz x(t) + dt dy dx z(t) = 0 dt dx + 3x(t) + 4y(t) + 3z(t) = 0 dt dt when x…

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Q: dx – x = 4y, UTM dt dy + x = y + 3e', dt

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Q: dy = 3. dt dz at (x, y) = (3, 1) and z² = x² + y² if dx = 1 and dt Find dz Preview dt

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Q: dy - 2y = 0, x(0) = 4, y(0) = 0 dt dx --x - 2y = 16te', 2x – dt

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Q: 4.Solve the pair of simultaneous equations dx =xy-t, x(0)=1 dt dy = x+t, y(0) = 0 dt From t=0 to…

A: You don't mention any method by which we can solve, so i use simple Iteration method Euler's Method

Q: Solve the following initial value problems using Laplace Transforms:

A: a.) The given initial value problem is,

Q: dy dy 6. = y³, y(0) = –2 dt 5. = y³, y(0) = 0 dt dy 7. dt = t(y² + 4), y(0) = 2 dy 8. dt 1+ y? y(0)…

A: Note: We will answer up to first 3 subparts. Please resubmit the question  which you would like to…

Q: dx If x2 + y2 + z2 = 9, dt dy 6, and dt dz when (x, у, z) %3D (2, 2, 1). dt 3, find %D %3D dz dt II

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Q: dx dy - x - 2y = 16te', 2x – dt - 2y = 0, x(0) = 4, y(0) = 0 dt

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Q: dy 2. Given: x y = 2x-3y + 2 and- 3D3 %3D dt dx when x = 2 and y = 1 dt Find:

A: Consider the equation.

Q: QI Find for dx dt dy 4e - 5x'e dx dy 3re + 5x'e" dx O 2, dy - 2e + 4xe dx dy 2xe dx dy dy 5x'er dx…

A: We have to compute dydx, where y=∫x6x5et2dt. Comparing the given integral with the equation…

Q: d²x dx (v) - 2 + 10x = e2t x(0) = 0, x' (0) = 1 dt2 dt

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Q: d?x dy -y = 0, dt? dt dx 2- dt dz +- z = 0, dt dx dy + 3x + dt -4y+ 3z 0; dt dx x(0) = 0, (0) = = 1,…

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Q: 3lne 9. -dx Integrate: S 25 3te 6t dt Evaluate: S VxV1+x/x dx y² +2y 10. 11. 12. Evaluate: J.…

A: Note: As per our guidelines, we are supposed to answer only first question. Kindly specify the…

Q: 2y +1 e'y 1+ y? dy dy = t*y dy 4. dt 2. 3. %3D dt dt t

A: See the answer below

Q: d² y dt² + 3 dy dt +2y(t) = 2e²¹ ; y(0)=0_

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Q: d³y dt3 dy + 4 dt2 + 5 dt + 2y = 10 cost y(0) = 0, y'(0) = 0, y"(0) = 0 %3D

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Q: dx —х +3у dt 13. Find the general solution dy -3x+5y dt ||

A: The objective is to find the general solution of system of differential equations…

Q: 2 Solue Bor メ= o-5 dx = y X (6) = 0 dt dy =_X yo) =I %3D

A: As per bartebly Guideline we can solve only one question.. Hope you understand

Q: 1. dy ==2(y+1);=3y-x+e³; t=0; x = 1;y=1 dt dx dt

A: SOLUTION: Given: dxdt=2(y+1)   ;  t=0;x=1;y=1dydt=3y-x+e-3t

Q: dy 1- dx e¯x-y-2 y(0)= -2 %3D dy 2- dx ylny %3D 1+x2 y(0)=e²

A: 1. ddxy=e-x-y-2,   y0=-2A first order separable ODE has the form of Ny·y'=MxRewrite, we get eyy'…

Q: dx 3x 6y = 0 dt dy 3x + Зу %3D 0 dt

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Q: - d² y dt² y (0) = 10 dy 4 - 5y = e-3t sin(4t); y (0) = 3, dt

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Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

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Q: d dt dx dy ruations dt - 2x +2y 1-2t, dyx-0. Giv dt 2 dt

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Q: III. Homogeneous DE 1. x dy + (y – 2x) dx = 0 2. (2x + 3y) dx + (3x + 2y) dy = 0 3. 3(x2 – y2) dx +…

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Q: What is the solution of given initial value problem? d²x = y + sin t dt2 d²y dx + cost dt dt2 æ(0) =…

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Q: dy for 2xy - 4x +2y3 = - 32, with the conditions dt dx 3 - 4, х%3D2, у%3 -2. Assume x and y are…

A: 2xy-4x+2y3=-32 Differentiating with respect to t, we get…

Q: d²y – 4y = 0 dy, - (at x = 0) = 4 dx а. dx? y(0) = 2; - d²y b. 5- dx2 sdy dy - (at x = 0) = 0 dx +…

A: To solve the given differential equations.

Q: dx = 5x + y; dt x(0) = 2 dy -3x + y; y(0) = 0 dt

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Q: If X+y = x-y x2. -y2 and dx/dt = 12, then what is dy/dt when x = 1 and y = 0? О 12 O -12 12

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Q: (i) (iv) (vii) dx x2 dx = (x + 1)(y² – 1) dx 1 –x² + 2x – 1 %3D = - | dt dt dt dy dy dy = x² – 2x +…

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Q: 1. dy = 2 – y²dx 2. x(1+x* )dy =(y +y x²-x* )dx 3. ( y² – 1) dx + (2xy – siny)dy=0 V2x-x2

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Q: d²y dx² -3 dy dt 4y = 3 sin x given y(0) ) = 0 and y'(0) = 0

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Q: dy a) -2y dx y = 2 sin x y = sin 2x y = e2x Oy = e-2r dy b) 2y dx y = 2 sin x sin 2x Oy = e2" y =…

A: Explanation and solutions is given below....

Q: III. Homogeneous DE 1. x dy + (y – 2x) dx = 0 2. (2x + 3y) dx + (3x + 2y) dy = 0 3. 3(x2 – y?) dx +…

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Q: dx 3D х — 2у dt dy dt 5x — у %3D x(0) = -1, y(0) = 5 x(t) %3D y(t)

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Q: d²x dx + 4- + 5x – 10 = 0, when t = 0, x = 0,x = 0 dt2 dt

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Q: y∅=y^-2 is the integrating factor of 2y(x+y+2)dx+y^2-x^2-4x-1)dy=0

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