What does Cauchys EU theorem guarantee for The IVP:  dy/dt = -(y)^2/2t,  IC: (to,0)

Q: Find the length of the curve r (t) = 3ti + square root of 3t^3 j + 2/3 t^3 k in [0,1]

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Q: Find the L^-1 iNVERSE LAPLACE d.)F(S) =3/4s

A: Inverse Laplace transform of (1/s) is 1 .

Q: Find the orthogonal trajectories of the famil y of curves x'yxy=c where cis constant

A: Given:    x3y-xy3=c      Differentiating by using power rule we get…

Q: 6) Find f(x) for f(x) = sec(vx2 + 1).

A: We are solving the first question and for the next question post the question again and alsomention…

Q: What is the laplace trasform of f(t)= (e^-4t)cosh4t

A: Laplace transformation is the integral transformation that converts a function of real variable to a…

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

Q: Consider The equation dy/dt = y^2(y^2-1) a-) Determine the equilibria and classify each one as…

A: Given autonomous differential equation is Here equilibrium points obtained from Now when .when when…

Q: tan y dy + In (secy) In (6)sec® de

A: Given data:     The given integral is: . The given integral can be written as, Assume Let…

Q: Hiw/ Find F'(x) 1 x, tanx if F(x) = X 2-if y= Sinx 3-Find y" (I)if yex) = Sec

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Q: Fied da のーーnfx+(2x +1 tar JE XーVEx+! 1-X

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Q: (2(1-2) (1--) dy dx dz 1-z) Evaluate S, a-2 (1-

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Q: Q4 A) Consider the i.v.p x' = t^(2) + cos(x), x(0) = 0. Verify that the hypothesis of Cauchy Picard…

A: The objective of the question is to verify the hypothesis of the Cauchy Picard theorem for the given…

Q: Solve the IVP: X' = AX, where --() 3 1 0 2 -1 0 0 A = 3 and X(0) = -1 2

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Q: Prove that da(x) = a(b) a(a), %3D |

A: This is a problem from Reimann Stieltzes Integral

Q: Laplace transform of the expression f(t) = sin

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Q: S*(1+v*) -\dv (cot-ly2) 2.

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Q: x2 + 8x +3 10) y=- _ dy A) 3x2 + 8x - 3 dx X Find the derivative. A) 11) s= t3 tan t-√√t ds dt C) dy…

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Q: Find the length of parametrized curve given by x(t)=12t^2−12t, y(t)=−4t^3+6t^2+9t where t goes…

A: Let us consider the parametrized curve x(t) and y(t)  The length of the curve is obtained as…

Q: g Solve Rour of the following D.E A)(xュ)dx + 2xy dy dy B) ャリ=ex c) (xx v y'es )dx -(y- )dy zo D) (X…

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Q: y"+2+y=e^5t y(0)=0 У (0)-5

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Q: parametrically

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Q: Q2/A/<he di fferential equation is yedx +3xay+dx +dyno diff erential when fineling the solution to a…

A: To find: The solution of differential equation y2dx+3x2y2dx+dy=0 and also find the constant (c) at a…

Q: Solve following Couchy probiem . the 2x e^uxy -Uxx +Ux =ye uloy) -0, Ux(0,y) =승 y %3D

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Q: prove that | Sinsy | dy лу ∞

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Q: Find the length of the curve r(t) = (ln(t))i + (2 t)j + (t²) k from t = to t = e.

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Q: if y³ - y = 2x Then, d'y -24y prove that dx (3y -1) |

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Q: arametrize the monkey saddle z=x^3−3xy^2 by using u=x,v=y as the parameters.  plot the image

A: Given equation is, z=x3-3xy2 Take u=x,v=y Then the equation becomes, z=u3-3uv2 The counter map is,

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.