3 (D2 + 4)y =- Ost<3 3t +2 t23 y(0)=0, y'(0)=1 Find L{y} °L{y} = 1 3. 3e 3s Se-3s 82+4 s(s2+4) s (s² +4) L{y} 3 3e 3s 1le-3s s(02+4) 2 (s² +4) s(s2+4) °L{v} = + 4) + F(+4) 1 3 3e-3s le-3s L{y} - 82+4 s(6?+4) s2 (s² (s2+4) °L{v} = 1+ % + 3e -3s 8e -3s %3D 8

Q: The dynamics of the variable ywith respect to variable xis described by the following stiff ODE: dy…

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Q: 2 Solve S dy Use u substibation with u=y² ¢ CLearLy show gamma function r (n+2) = nTn) propeaties

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Q: Match the differential equation with its direction field. y' = 9(x + y) - 1 15 0.1+ -4.31 -0.2 -Q.1…

A: Matching the differential equation with its direction field  y'=9(x+y)-1 x 0 0 0 0 0.1 0.2 0…

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A: The given partial differential equation is ∂y∂t=2∂2y∂x2 where y(0,t)=y(5,t)=0 and y(x,0)=10sin 4πx

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Q: 4. (ye"-2y)dx + (xe-6 xy- 2y)dy = 0; x = 0 when y = 2. 5. (x+3) cos y dx - (sin y In(5x + 15)-y} dy…

A: The exact differential equation for the equation, F(x,y)=C, is written as Fxdx+Fydy=0, where, Fx ,…

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A: The given problem is find the solution of heat equation with given initial conditions and boundary…

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A: Consider an IVP y''+p(x)y'+q(x)y=f(x). The initial conditions are y(x0)=y0 and y'(x0)=y0'. Then if…

Q: Find the differential dy: y = In(sec² ( 3"-2*+5)). Find the differential dy: y = In(sec? ( 3-2x+5…

A: We have to differentiate given function

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Q: dy Kutta method to integrate = 4e0.8x step size of h 0.5 and an initial condition of y = 2 at x =0…

A: 4th order Runge-Kutta method…

Q: In (A) y = 3" (B) y = 3* (C) y = -3* (D) y = -3*x (E) y = 3* – 1 (F) y = 3*-1 (G) y = 31-x (H) y = 1…

A: Assuming  f(x) as a exponential function Then by shiphting

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A: The given differential equation is,(y2e-2x+3x2-x)dx-(siny+ye-2x+3yey)dy=0, x(0)=1

Q: (b) f(x, y) = 3.03 + 3y2 – 4 ln y, a = 0, y = 1, dr = 0.01, dy = -0.01. since fa (x, y) = 3.3x-1+ 0…

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Q: 17. Using Runge-Kutta method of fourth order, solve dy y2-x2 dx y2 + x2 | with y(0) = 1, at x = 02…

A: Numerical methods: Ruge-kutta method

Q: dy Use 4th order Runge - Kutta method to integrate step size of h = 0.5 and an initial condition of…

A: Let dydx=f(x,y) and the initial condition is y0=f(x0) . The 4th order Runge-Kutta method uses the…

Q: OBTAIN A FAMILY OF SOLUTION 2. (x - yny + y In x ) dx + x CIn y - In x)dy =0 3. [x - yarctan…

A: This question is related to differential equation.

Q: 8.2 Making the change of variable z=cos(x) in the equation y" - y' cotx - y sen²x = 0,, the equation…

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Q: y=Ax+Dx^B is the particular solution of the first-order homogeneous DEQ: (x-y) = 5xy'. Determine…

A: Given differential equation, 5xdydx=x-y,  x=3,y=6 dydx=x-y5x put, y=vx dydx=v+xdvdx now put values…

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Q: (a) The reaction to form an iodine molecule is a second-order kinetics rate of loss of iodine atoms…

A: Find out the value of I after 1.5 seconds.

Q: Compute Y (II) withe y" y'= -8 (Sinx+cosx. Y(T) = 0, y¹ (F) --8, by @ Taylor Series

A: Given differential equation is y''-y'=-8(sinx+cosx)     (1) and y(π)=0, y'(π)=-8 Solution a: Using…

Q: 1. (2xy-tany)dx + (x² – xsec?y)dy = 0; y(1) = r 2. [4x°cos(xy)-x*ysin(xy)- ye" +3x²]dx…

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Q: (a) The reaction to form an iodine molecule is a second-order kinetics rate of loss of iodine atoms…

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Q: 2. Consider a homogeneous differential equation, p(т, у) dx + q(z, у) dy %3D 0, where the…

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Q: The dynamics of the variable ywith respect to variable xis described by the following stiff ODE: dy…

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Q: 2t-4 0st<2 (D2 - 1)y = t22 y(0)=0, y'(0)=1 Find L{y} L (1) = 1 + - - 2+ 4 2e 2s 2e-2s %3D | L (y) =…

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Q: 2) (2x + sin x) dx + x cos y dy = 0 3) - 2y + a = 0 dx dy 3y 4) r2 (Exact). (Separation variables).…

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: The dynamics of the variable y with respect to variable x is described by the following ODE: dy –x²y…

A: Runga-Kutta Method of order 4:

Q: (1+x^3) dy-x^2ydx=0 satisfying the initial condition x=1, y=2

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Q: cos v f(x, у, 2) 3D xz2 af af 2 cos y Cosv siny df = - = - = - dx x2z2' dy dz xz3 XZ af cos v %3D af…

A: Topic:- partial derivatives

Q: 2t – 4 0st<2 (D² – 1)y = [2 t 2 y(0)=0, y'(O)=1 Find L{y} O L 1) = + -1) 2e-2s +. s(s² -1) 4 2e s2…

A: To solve given question first we take Laplace transform of both sides and solve.

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: 3. [cos y + 1]dy + [tan x (sin y + y)]dx = [sin y cos x + y cos x]*dx gettyimages Fuse When:x = 0; y…

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Q: 2. y' = y sec x ; 3. у(3x3 — х + у)dx + x?(1 — х?)dy %3D 0 4. у(2х — у + 1)dx + x(3x — 4у + 3)dy — 0…

A: 2) y'=y secx this can be written as dydx=y secx⇒dyy=secx dx integrate the function ∫dyy=∫secx dx…

Q: Consider the Initial Value Problem (IVT) dy = Axy, y(0) = 1, da where A is a positive constant. The…

A: As per the rules we can solve only 3 subparts. Please check the below answers

Q: 1 transforms the equation x dy + y = xy2sin(x) into The change of dependent variable y = dx dv A.…

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Q: 2 f(x)cos(n@,x)dx = %3D 27 cos(nx)ch. sin(nx) cos(nx) (2x) -sin(nx) + 2 11 f(x)sin(n@,x)dx =- [x…

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Q: The temperature u(x, t) of a metal bar of length (= 2 at a distance r from one end and at time t is…

A: Image is attached with detailed solution.

Q: (b) Evaluate 18x²y² dx dy where D is the bounded region enclosed between the curves y = 2/x², y =…

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Q: 6. Find S(3y – y³) (1– y?)dy sin ycos y 7. Integrate: J sin² y dy 8. Find 3 S(5 - 3y-5)²dy

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Q: What is the solution of given initial value problem? y+sin t dt d'y dz +cos t (0) = 1, z'(0)-0,…

A: We will find out the required solution.

Q: 01 (test for exactness) * 4 points (siny - ysinx) dx +(cosx +xcosy) dy =0 01 (solve exact de) * 4…

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Q: Obtain the particular solution when x = 1 and y = 1 y(x^3-y^-5)dx-x(x^3+y^5)dy=0

A: Here is the solution of the given differential equation.

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…

A: