Solve for F(x) the integral equation F(x) sin xt dt = {2, 1

Q: dx xt x(1) = 2, solve for x(2) when h = 0.1 %| dt t²+2

A: As per the question we have to solve the following first order differential equation : dy/dx =…

Q: That the value of the integration g(1) = 00 , g(2) = 0 1-e t) -dt 9(t) where g is a function that is…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s).

A: Explanation: Given that,  f''(x)=sinxf'(0)=1f(0)=6       Concept Used:

Q: Find the particular integral of the differential equation belov (D² + 1) y = sec x tan x

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Q: The order and degree of the partial differential equation respectively 6 9. dz + sin x = xy? is_ %3D

A: Given,          ∂4z∂x46+∂z∂x9+sinx=xy2

Q: y" – 2y' + 5y = 8e'sin2t, y(0) = 1, y'(0) = -1 %3D

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Q: Solve the integral equation y(t) cos t + y(x) cos(t – x)dx %3D

A: The given integral equation yt=cost+∫0tyxcost-xdx can be written as  yt=cost+ytcost Now apply the…

Q: Use the method of variation of parameters to solve the given non-homogeneous linear ordinary…

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Q: dy/dx − x^3 = 0 where y(0) = 5

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Q: The order of the differential equat 2x2 - 3+y = 0 dy + y = 0 dx2 dx O not defined O 2

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Q: Linearize the following differential equation about point, x= T/3. d²x +2 dt? dx + sin x=0 dt

A: Answer:

Q: Find the solution of the differential equation that satisfies the given initial condition. y' tan(x)…

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Q: dx 1. dt xt x(0) = 1, solve for x(0.3) when h = 0.1 I| -

A: Given function is, dxdt=-12xt,   x(0)=1, h=0.1 and we need to solve, x(0.3)   Here we have, (t0,…

Q: 6) Solve the homogeneous differential x2 + y? dy quation dx 2xy

A: on solving this we get

Q: (A) Find the integration factor of the non exact differential equation 2y e +2y dy 0 +1 dx +

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Q: dx 2. dt x(0.5) = 1, solve for x(1) when h = 0.1 2(t+1)

A: It is given that, dxdt=x2(t+1),    x(0.5)=1, h=0.1 and we have to find x(1)   Here interval is 0.1,…

Q: (t + z cos(t)) dt + (sin(t) – 3z2 + 5) dz = 0

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Q: (4) Using Convolution, Solve the Volterra Integral Equation: y(x) = 1 – e-" + y(x – t) sin a dt

A: Given Volterra Integral equation: y(x)=1-e-x+∫0xy(x-t)sinxdt Using convolution it can be written as…

Q: The integrating factor for the differential equation dy X- dx 4x cos(x)y = –5e* is e-4 sin(x) Select…

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Q: f1-p, 01 Solve the integral equation F(x) cos px dx Hence deduce that Sin dt 2

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Q: 7. Find the differential dy for y = x2 – 4x + 6, then evaluate it when x = 2 and dx = 0.1 -

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Q: - (v + x³ + xy®)dx – xdy = 0.

A: To solve the given differential equation.

Q: Determine whether the family of functions x = c, sin t + c2 cos t is a solution of the differential…

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Q: 87. Find the value of dy/dt at t = 0 if y = 3 sin 2x and x = t+pai

A: Given, y=3sin2x,  x=t+π y=3sin2t+2π we know, sinA+B=sinAcosB+cosAsinB sin2t+2π=sin2tcos2π+0=sin2t…

Q: Show that y = x+vx +1 satisfies the differential equation (x + 1)°Y + x°Y. ydy -m³y 0 + X- dx2 dx

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Q: Determine the integrating factor for the differential equation y dx - x dy = 0. А. 1/х3 В. —2/x2 С.…

A: follow next step

Q: The differential equation (-xysin x+2ycos xdx +2xcos x dy 0 is

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Q: Solve the differential equation dx 7x In x dt t Assume x, t > 0, and use the initial condition x(1)…

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Q: . [1+ y tan(xy)]dx + x tan(xy)dy = 0

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Q: The particular solution of the differential equation dx x + Int when t = 1, x = 3 is dt a. x = 4t –…

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Q: dy The integrating factor of Linear differential equations + y x 4tan ¤ = sec²x is_ dx In cos 4x tan…

A: The coefficient of y is: P=4tanx So the integrating factor is: e∫Pdx

Q: The integrating factor of the differential equation (x+x sin 2y) dy =2y dx js: A x-3

A: We will find the integrating factor as shown below

Q: Find the differential dy of the given function. y = V 3 - x2 dy =

A: Find derivative

Q: a). Sketch the slope field of the differential equation. (x - y); within the Interval -3 ≤ x ≤ 3 -3…

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Q: Use the method of asymptotic expansion to find the asymptotic solution of the differential equation.…

A: We will use the basic knowledge of ordinary differential calculus to answer this question completely…

Q: Find the general integral of the partial differential equation (y² + yz + z²)p + (z² + zx + x²)q =…

A: Given :-  The general integral of the partial differential equation  y2 +yz+z2p + z2 + zx + x2q = x2…

Q: Find the general solution of the differential equation y + wóy = cos ot, w² w%. Use C1, C2, C3,...…

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Q: Solve the separable differential equation dx 5 dt and find the particular solution satisfying the…

A: Given that:dxdt=5xx0=4To find x(t)

Q: Use the method of steps to solve the delay differential equation dx x(t – 1) + 3; x(t) = 1 V…

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Q: 8. Solve the Volterra integral equation y(x) = cos(x) + y(t)dt

A: Given integral equation is yx=cosx+∫0xex-tytdt                           (i) Differentiating both…

Q: Determine the differential equation whose integrating factor is x2 A (2у-3x) dx + х dy%3D0 B В y dx…

A: Suppose we have the first order differential equation dydx+Py=Q,where P and Q are…

Q: Find a continuous solution satisfying the differential equation and the given initial condition. dy…

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Q: Find the solution of the differential equation that satisfies the given initial condition. y' tan(x)…

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Q: Find the particular solution of the differential equation that satisfies the initial condition(s). f…

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Q: y' tan x = a + y, y(T/3) = a, 0<x< T /2

A: If a differential equation is given, then isolate the similar type of variable on one side. Then…

Q: =x+x* +1 satisfies the differential equation (x +1): dy Show that y dx

A: Given the given differential equation is x2+1d2ydx2+xdydx-m2y=0 and the given value is y=x+x2+1m.

Q: F- Show that the partial differential equation du du 0 has the general solution u(x, y) = e"[f(x) +…

A: We will prove the following result.