dx -5x² – xy + 114.x dt dy -x?y – y + 900y dt Find the equilibrium points in the first quadrant

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

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Q: dy dx ; x = 0, y = 1 , t= 0 dt dt 2) x = t2 + t y = t2 -t -00 <t < 00 %3D fall

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Q: e-Using dy dx dt + Зу -5х —е t — dt dy +x+y- 3 = 0 dx dt dt

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Q: Determine whether the equilibrium at x = 0 is stable, unstable, or semi-stable. dx = 3x7 dt The…

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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: y = 2x2 + 9; (a) x = -1 (b) x = 0 (c) x = 1 dx dt of the given function at the rate dx/dt. Find…

A: The main objective to calculate the value of dydt for different values of x.

Q: dx -y = 5 dt dy = 3t dt 2x -

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Q: d²x 1. dx +9x =0. when t-0, x-2 and dt dt dt

A: Note: since you posted multiple question. As per our guidelines we are supposed to solve one at a…

Q: dy Find dx 4t t dt + 2 y = dt - t° + 2 - 3 6. dy dx (Simplify your answer.)

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Q: dy dx Given y=x³ - 2× and = 3. Determine the value of dt when X=2. dt

A: Differentiate the equation y=x3-2x with respect to t. y=x3-2xdydt=3x2dxdt-2dxdt=3x2-2dxdt

Q: y3 r³ – 4x – 1 = 0 3 Find dy/dx and explain why dy/dx is always positive. Where on the interval [0,…

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Q: dy 5. dt = e&-t)secy(1+ t²). %3D

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Q: = y – 2², dt dy = y - ar. - у — dt For parameter a, classify the equilibrium points when a>5

A: Both the equilibrium points (0, 0) and (a, a2) are saddles.   Explanation: Let   First, we find the…

Q: y = 2 (x² – 3x) (a) Find dy/dt when x = 2, given that dx/dt = 4. dy/dt = (b) Find dx/dt when x = 9,…

A: First we will derivative with respect to t then find both value

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

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Q: 2 4) d?y |1+ () dx2 dx, Find the: Туре: Order: Linearity: Why?: Unknown Function: Independent…

A: Topic:- differential equations

Q: dz = arctan ду G) dz Find: dx 2x 2y dx x²+y² x²+y² dx dz y %3D = dx x²+y² dx x²+y²

A: given,        z=tan-1xy

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: dx %-D5 when x= 4. dt ,3 Assume that x x(t) and y y(t). Let y=x +2 and dy when x= 4. Find dt dy…

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

A: The given differential equations are                                  dxdt-x-2y=16tet ..............…

Q: dx = 3x + 2y dt dy -2x + 3y dt

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Q: Solve dy = x'y° - xy t. dx %3D .3

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Q: 3tarx - (2x-3y 14)dx + 3x-1) dy =0 2 cory) sec'x dx t tanx 1, wheh X= 3 y=z

A: Let's find.

Q: dx dt Please give an exact answer. dy = 2, dt If z³ = x² + y²₁ Provide your answer below: = 1, and…

A: Given problem:-

Q: (* y²+x?y²+x2 x?y ) dx =dy +dy-x dy

A: Explained below

Q: (xy+y2) + (x2 -xy)(dy/dx) Homogeneous equations

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Q: Ex.: Solve dx dy 2- dt -x- e' dt dy dt dx +2. +y%3Dt.. dt versity-Civil Enginee & Num. A

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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: d’y_2dy 3 y=2sin°(x) dx Determine the general solution of 2 dx

A: We have to determine the general solution of the differential equation…

Q: dy when x = - 1 and dt dx Given y = 6x + 7x, find = 3. dt dy (Simplify your answer.) %3D dt

A: dy/dx=(dy/dt)/(dx/dt)

Q: dx = -y+y(x² + y² dt dy = x – x(x² + y²) - dt

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Q: dx dy dy Find and dt' dt dx x = 3t – 3ln(t), y = 4t2 – 4t-2 dx dt dt dr

A: Given x=3t-3lnt        y= 4t2-4t-2

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: d²y 35. Find dx2 of x² + y2 = 1 implicitly. %3D

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Q: Determine whether the equilibrium at x = 0 is stable, unstable, or semi-stable. dx 3 dt The…

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Q: dy The equation dx x2 (1) +1 is a separable equation. 1- y? (m) For the equation y dx + (2x – ye")…

A: To find Whether the given statement is true or false

Q: : Solve-Using D-operator dy dx + 3y – 5x - e-t = 0 dt %3D dt dx dy 2- dt +x +y-3 = 0 dt

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Q: b. (xy - y)dx + (x² – 2x + 3y)dy = 0; when x = 1, y = 1

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Q: rV1-y² (x² + y³) dy dx -1 J-V1-y

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Q: 3. (y – 2)dx – (r - y – 1)dy = 0 (coefficients linear in two variables) %3D

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Q: dy Va2-x2 with initial condition y(a) = 0. dx -a va2-t2 dt This can be solved by y = J %3D II

A: From the above question, we get the differential equation dydx=-a2-x2x with the initial condition…

Q: Solve: y""(t)- y" (t) + y' (t)- y(t) = H(t); y(0) = 0; y'(0) = y" (0) = 1; where H(t) (t+3,0 ≤ t <1…

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Q: Q3. Find the value for a, b,c and d so that the fixed point ( the origin ) of dx ax + by dt dy = cx…

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Q: dx (b) (t– 2) – x = (t – 2)' , x(4)=10 dt dx (c) +5x -t = e" , x(0)= dt

A: Here we have to solve given initial value problem b and c.

Q: dx Given y= e-2x? dy when X = 1 and dt 2. Determine the value of dt

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Q: z = x+ y dy _ x+ y+2 1. Using substitution solve the equation which satisfies the condition y(1) =1.…

A: Use the given substitution to convert the homogeneous differential equation into separable form then…

Q: z = x+ y dy_ x + y +2 1. Using substitution change the dx x+ y+7 to a separable equation, Hence…

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Q: Find the solution y = y(x) of y2 dy + y - dx = 0, x3/2 subject to y(1) = 1.

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Q: 3X-Y-4) dy wheh X=4 i y=l ty dx

A: You can solve by any method