Q3. Find the value for a, b,c and d so that the fixed point ( the origin ) of dx ax + by dt dy = cx + dy dt is a 1) source node (1i) sink node (ii) spiral source (iv) spiral sink (v) saddle point Solution: Try it yourself

Q: 9. dy/dt = y²(y² - 1), -∞ < Yo <∞

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Q: use Separation of Variables to find the general solution. dx/dt= (t + 1)(x2 + 1)

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Q: I'm stuck on this question and I don't know how I should be approaching this. What should I do?

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Q: Find the general solution of

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Q: 3. Determine the coefficients a, b, c, d that will make the curve y = ax³ + bx? + cx +d have…

A: We will find the value of a, b, c, and d as following .

Q: Q-23 (aT trajectories of the families of y? = 2ax, where a Find the orthogonal being a parameter.

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Q: 7. Given: y = 3 ; Find: dy/dt V16+tª -613 (16+t*) -2t3 (16+t*) (16+41) 글 (16+t*) ? (E) None of the…

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Q: d²y 1 dy y + y(3) = 0.009u, y(10) = 0.003s - dt2 t dt Use an appropriate method to find y(t).

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Q: (6) Find the orthogonal trajectories of the family of curves r= 2C cos 0, where C being parameter.

A: Consider the given curve. r=2Ccosθ          (1) Find the derivative of the given equation.…

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

A: Answer is mentioned below

Q: 16 Q4- Solve the following system of ODE dx dt Eaux"> dy dt = y + 1 =x+1

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Q: dy + 2y = 5t dt %3D For the initial condition y(1) = a, give the domain over which the solution is…

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Q: Find the value of C so that y(t) = Ce2t satisfies the initial condition y(1)=1

A: Substitute t=1

Q: 2 4 find the orthogonal trajectories to c¯y y" = 4y´ + x´ 2 2 .... ..... ..... .....

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Q: 2. (a) Find the linear approximation L(x, y) near the point (1, 2) of the function f (X,Y)=(0=Y) +…

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Q: 02/ Solve the system derivative to find the general solution of each (x & y as a funtion of t). dr…

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Q: Solve the DEQ given the initial condition (2,0). Graph it on the slope field. 11 « 10 Let…

A: dydx=g(x,y)g(x,y)=ey(3x2) - dydx=ey3x2Separating the…

Q: Find the orthogonal trajectories of the family y = 1 - sec?r + C 4

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Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1) = 8

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Q: Show that if

A: To Determine: show that      dydt=ky1-y Given: we have y=11+be-kt Explanation: we have  y=11+be-kt…

Q: (6) Find the orthogonal trajectories of the family of curves y = ax? + 4ax + 4a, where a being…

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Q: Q4: Find the general solution of d?y dy - 3 - 4y 3e2t + 2sin t - 8et cos 2t, dt dy y(0) = 2, (0) %3…

A: Given that  The differential equation  To find the general solution

Q: 2. Find dy/dx a) y = dt, x> 0

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Q: Determine the constants c and d in the equation of the curve y = at (0, -1) and an inflection point…

A: This question can be solved using the concept of functions and derivatives.

Q: 2e | 3జy S S dy da = Vsin(zy)

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Q: If y is a function of x, then the equation (y - a)dx + 3ry dy = 0 is not linear + but both + and…

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Q: 13. dy/dt = y²(1-y)², -∞ <yo <∞

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Q: _1. y +1-2 dy, can be evaluated conveniently if we let y+1-2=t and dy = 4r(r +2)dt. %3!

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Q: dr = -4rt whent=0, r=r, dt Obtain the particular solution of - %3D

A: we have to use separation of variable

Q: Show that y = e^2t is a solution of y’’’ - 2y’ - 4y = 0 (where ‘ denotes d/dt), and find the general…

A: We need to solve differential equation and show that y = e^2t is a solution.

Q: Suppose that a projectile is fired straight upward from the surface of the earth with initial…

A: velocity v = rate of change of displacement y Hence, v = dy/dt Hence, d2y/dt2 = dv/dt = (dv/dy) x…

Q: Solve the IVP dy/dt + 2(t + 1)y^2 = 0, y(0) = −1/8

A: To solve the IVP dy/dt +2(t+1)y²=0, y(0)=-1/8

Q: Q1\ Use Runge-Kutta method with (h=D0.1) to solve the equation y+ 3xy - 6y = 0 ; given that yo = 1…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Q.2, a, Solve he initial valve problem * (2+x) dy + 2(1+x)y = 1+3x² y(-1) = 1 %3D by Find an…

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Q: 4. Transform the equation y'= f(x)dx+ f(y)dy = 0. 2xy Into the form of varlable separable…

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Q: What is the equation of the curve y = ax* + bx + cx² + dx + e tangent to y = 25x (2,14), to y = 2x +…

A: By verifying options and substitution of point (-1,11) it is verifying option C

Q: 2. Determine the solution of y dt + (2yt + 1) dy = 0given that given that y (-1) =Q

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Q: Q5) Solve the equation dx dt² 1 y (x,0)=sin лx ,t=0,0≤x≤1 8 and dy (x,0) =X at 11 with y (0,1)=y…

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

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Q: dx 2x - y dt dy

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Q: you make for the particular solution to the linear. non-homogeneous dt 10y Te Your answer shotld…

A: Non homogeneous differential equation.

Q: ind the orthogonal trajectories of the family of curve x2/3 +y2/3 =a2/3 where "a" is the parameter

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Q: solve the simultaneois equation (dx)/(dt) = 3x + 2y (dy)/(dt) + 5x + 3y = 0

A: Given simultaneous equation, dxdt=3x+2ydydt+5x+3y=0 The eigen value of a matrix is calculated by…

Q: (6) Find the orthogonal trajectories of the family of curves r= 5C cos 8, where C being parameter.

A: we have to find the orthogonal trajectory for the given function

Q: dy dy + 7 dt + 10y = e-t dt2

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Q: Q2) Solve the following problem over the interval from x = 0 to 1 using a step size of 0.25 where…

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Q: 8. Find the solution y(t) of th d³y dy - 2y% = dt dt3

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.