47x +75y -30x - 48y satisfying the initial conditions r(0) = 19 and ly' y(0) 12. x(t) = y(t) =

Q: Find the solution of the initial value problem with zero initial conditions ý – y + N f(t)dt = eNt…

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Q: Verify that 1 $(x, y, z) = satis fies the partial differential equation x² + y² +z? = 0 ax2 ay2 "…

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Q: 2 What is the solution of the initial – value problem d²y =X O with y(0) = 1 dx? and y'(0) = -2 ? у…

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Q: Find the solution of the initial value problem with zero initial conditions ý – y + N| f(t)dt = eNt…

A: We have to find the solution of the following problem for N=80: y'-y+80∫0tftdt=e80t with the initial…

Q: 3. Apply Euler-Maruyama method as one step to solve the SDE 3 y dy dt + dBt 5 t y(1) = 2

A: Given dy=3-y5-tdt+dBty1=2

Q: y'' + 4y" + 5y' + 2y = 0 y(0) = y'(0) = 0, y"(0) = 4

A: The solution is given as

Q: Let y be the solution of the initial value problem y′′+y=−sin(2x), y(0)=0, y′(0)=0. Find the maximum…

A: Here, differential equation is y’’+y=-sin2x

Q: Solve the partial differential equation: a²u =²; by the method of separation of variables for a…

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Q: How does the Fundamental Theorem provide a solution to the initial value problem dy/dx = ƒ(x), y(x0)…

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Q: A mass-spring system is modelled by the differential equation u' + 16 u = 0, and the motion starts…

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Q: 7. Find the solution of the differential equation using Laplace Transform. y" – 3y' + 2y = e3x when…

A: We need to solve DE.

Q: a. Can y, = 3 – t2 and y2 = 4t3 be both the solutions to a differential equation y" + p(t)y' + q(t)y…

A: (a) Consider the provided question,

Q: Solve the initial - value problem : dy = Cos x - Sinx +y, 0 sx < 0.5 , y(0) = 0 dx using (a) four-th…

A: Given differential equation                                                dydx=cosx-sinx+y,…

Q: The differential equation y²x + 2y'eª = 0 is Select one: Linear Exact Seperable Homogeneous

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Q: 2. Verify that y = -t cos t – t is a solution of the initial-value problem dy = y + t²sin t dt y(7)…

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Q: Approximate the solution of dy _ y-1 dx x+3 %3D with initial condition y(-1)=0 for –1<x<0 by using…

A:

Q: Make a phase diagram indicating whether the critical points correspond to an attractor or a repeller…

A: We need to create a phase diagram (slope diagram) and analyse its behaviour at the critical point.

Q: Solve the initial-value problem with the initial condition Yo = 0. dy y + 3 dt %3D y =

A:

Q: 4. At high temperatures, nitrogen dioxide, NO2, decomposes into NO and O2. If y(t) is the…

A: Given: y(t) changes according to the law, dydt=-0.05y2 where, y is the concentration in moles per…

Q: Solve the initial-value problem: dy cos x - sin x + y, 0<x< 0.5, y(0) = 0 dx using a) Fourth-order…

A: Given function is                                                   dydx=cosx-sinx+y, 0≤x≤0.5 with…

Q: Let y be the solution of the initial value problem y" + y = – sin(2x), y (0) = 0, y' (0) = 0. The…

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Q: (b) Find the general integral of the partial differential equation dz dz. = 7., X- which contains…

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Q: I Example 10.18. Using Runge-Kutta method of fourth order, solve for y at x = 1.2, 1.4 dy. 2xy + e*…

A: Given y' =(2xy + e^x)/(x² + x e^x), initial point y(1)=0 To find y(1.2) and y(1.4)  Let step size h…

Q: 4. Solve the initial-value problem dr = -2r - 2y dt dy -2r + y. dt where the initial condition is…

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Q: Express the solution of the given initial value problem in terms of a convolution integral y" + 12y'…

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Q: 11. Solve the initial-value problem dx = -2x – 2y dt dy -2x + y. dt where the initial condition (x…

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Q: Solve the initial value problem: y' + 4y = sin t – u2n (t) sin(t – 2x) y (0) = 0, y' (0) = 0

A: To solve the given initial value problem we will use Laplace transform. For this we require few…

Q: You can think of the first two cases as being performed in vacuum (no friction) and air of water…

A: Let's find.

Q: The approximate value of y(3) for the initial value problem for dy/dx = cos(t) +sin(t), y(0)=0.5…

A: 4th order Range-Kutta method: The solution of y'=f(t, y), y(t0)=y0 is given by,…

Q: Approximate the solution of dy _ y-1 dx x+3 with initial condition y(-1)=0 for –1<x<0 by using Euler…

A: The numerical solution of the differential equation is the value of the function that satisfies the…

Q: Discretize the differential equation y' =1– 2t , y(0) = 0 over the interval [0, 2] with step-size h…

A: Given differential equation y'=1−2t, y0=0 over the interval 0,2 with step size h=23 Where, y2=y0,…

Q: 3. Approximate the solution to the partial differential equation a²u ²u 5л 0x2 (x, y) + dyz (x, y) —…

A: Given: ∂2u∂x2x,y+∂2u∂y2x,y-12.5π2ux,y=-25π2sin5π2xsin5π2y To find: Dirichlet boundary condition

Q: What are the equilibrium solutions of the DE dy /dt=−3(2−y)?

A: given DE  is dydt=-3(2-y)

Q: Q8. Classify the following Partial Differential Equation Ury - Uyy ,+ 2Uz = 0

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Q: Verify the function y = xe^-x + 2 is a solution of the initial value problem: dy/dt = (1-x)e^-x when…

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Q: Find all the critical points (equilibrium solutions) of dx dy = y+ 5xy. dt dt

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Q: 2(a) Given that f(x, y) = 6x²y3 – cosx + 5y – siny + 10x, establish the fact that, the order in…

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Q: Solve for the solution of the given Partial Differential Equations with boundary conditions. Əri =…

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Q: Solve the initial value problem. nt 7y – 2y = e-, y(0) = Let a, be the value of a for which the…

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Q: (a) Find and classify all the equilibrium solutions for the given differential equation 3 = y – y –…

A: a) To find and classify the equilibrium solutions of y'=y3-y2-6y b) To find the orthogonal…

Q: dt 4. Solve the initial-value problem dx = -2x – 2y dt dy = -2x + y, dt where the initial condition…

A: To find the solution of the given system of differential equations.

Q: 1. e (3xy-x)dx+e* dy = 0; when x = 0, y = -1 4 Ans. y =-- 1 3

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Q: Solve the initial value problem from t = 0 to 2 when y(0) = 1. %3D dy yt³ – 1.5y dt -

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Q: Use Euler's Method to approximate the solution of the initial value problem.  dy/dt=t-y…

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Q: In - dy + (csct) y = ²n (- + == ), 4(-4)=3 1 -7²-25 dt

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Q: Q-1-) Eind the general solution of the given Ordinary Differential Egauations system: X'(t) = *(1)…

A: Given: X¯'(t) =3-94-3X(t) where X¯(t) =x1(t)x2(t) To find: General solution of given system of…

Q: Consider the autonomous first-order differential equation y = y(y +4)(y – 5) (a) Find the critical…

A:

Q: 3. Apply Euler-Maruyama method as one step to solve the SDE 3 y dy = dt + dB 5-t y(1) = 2

A: Given the SDE is dy=3-y5-tdt+dBty1=2

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

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Q: btain the differential equation of the given family of curve: y^2=x^3/(c-x) O A. x^3 y^'+x^2 y+y^3=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.