ds Differentiate with respect to t and solve for dt s2 = x² + y? %3D 2s ds dt = 2x + 2y dt dt x + ds dt dt %3D dt

Q: Given y = 3x2 and x = t2 - 1, find dy/dt for t = 1 %3D 1) 3 2) 6 3) 0 4) 12

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Q: d'x dx Solve the equation + 2x = e given that x (0) = 0, x' (0) =1. +3 dr dt %3D

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Q: The solution of: v(t) = e =t + ] sin(t - T)y(T)dt , in terms of convolution is:

A: Convolution theorem of Laplace transform    Laplace transforms of the functions Inverse Laplace…

Q: Solve the following differantial equation using finite difference method. d²x(1) + x(t) = 0 dt? dx…

A: Consider the given DE and finite difference formula for the function x(t).

Q: 1. Solve the DE as follows: d'y dy +3. +2y = 24 y(0) = 10 and y'(0) =0 dt? dt

A: Note :-  As per our guidelines , we will solve only first question for you. If you want any specific…

Q: Find an integrating factor for the linear DE of order one dx + (2xy – 1)dy = 0. (1)y? ... (2) ev²…

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Q: d²x_dx Verify that x = C,e¬t + C2e2t is a solution to dt2 2х — 0. - dt

A: To verify the given statement.

Q: 2. Determine the solution of y? dt + (2yt + 1) dy = 0given that given that y (-1)=Q %3D

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Q: The special integrating factor of y'dx+(3xy + y² -1dy = 0 is: a. e3y b. Зу С. У d. y-3

A: Solution

Q: Solve the DE as follows: d²y dy +3+ +2y=24 y(0) = 10 and y'(0) = 0 dt? dt

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Q: Find an integrating factor and solve the equation у da + (3гy — e Sу) dy %3D 0. -

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Q: Solve the following differantial equation using finite difference method. d²x(1) + x(t) = 0 dt? dx…

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Q: dy + 2(t + 1)y² = 0, y(0) = – }. 4. Solve the IVP dt

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Q: Solve the DE by Variation of Parameters (D³ + D² – 2D) y = 4e 2" cos a Cos r y (0) = 0.4, y' (0) =…

A: given (D3 + D2 − 2D)y = 4e−2x cosx The auxillary equation is m3 + m2 – 2m= 0 m(m2  + 2m - 2)=0…

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: dy 3. + Ay = w; y(0) = 0 and A> 0 dx

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Q: The general solution dx/dt t+x of t > where t > 0, is x(t) =

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Q: b. g(x) = [ cos(r*)dt x²+5x F(x)= [,(6r* +6e° )dt с. 6t +6e" dt

A: We have to find derivative

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

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Q: d Evaluate In(et – t²)dt. Briefly explain your answer. dx '1

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Q: Solve the given equation using an integratingfactor. Take t > 0. 6y′ + ty = t

A: the given differential equation is: 6y'+ty=t we have to solve the given equation using an…

Q: dx —х +3у dt 13. Find the general solution dy -3x+5y dt ||

A: The objective is to find the general solution of system of differential equations…

Q: Find the general solution for y(t) where; dy a. dt + 6t?y = 2t2 dy b. + 10y = 0 dt

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Q: dx/dt = t+x t> 0, The general solution of x(t) = where is %3D

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Q: Q/ Solve the D.E.: d'y dy 2 + 2 - y = 0 dt2 dt

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Q: The integrating factor of + 2xy= 5x² is dx dy а. b. x? e C. 1 - d. et

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Q: 2. Variable Separable eyx a) dy =D dx ey+x?ey

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Q: 4d'y dt? dy -8y= 8e, find the solution dt a) Using the Method of Variation of Parameters

A: Given differential equation is 4d2ydt2−4dydt−8y=8e−t....1 We have find the general solution by using…

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: Find - given that dt dx x? + y? = 2x + 4y, x = 3 y = 1, and dt 11 dy i dt II

A: Given problem is :

Q: (ztan 2 +1) dx – x dy = 0

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Q: Determine whether the given equation is separable, linear, neither or both.  (t^2+1)dy/dt=yt-y

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Q: Solve the IVP 3 d.x dx a(0) = 1, = 2. dt \t=0 dt2 dt

A: Given d2xdt2=-x(dxdt)3, x(0)=1, dxdt|t=0=2

Q: E. Find , and in terms of dx dt' dt 1. x = t°- 1 2. x = 4t + 3 y = 3t – 2 y = 4 - t

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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: Find the solution of ty -1 dt t'y 1 dy = 0 ty? O In t + 1 C ty %3D O -t-2 + 1 = C ty %3D Ct

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Q: . Is sin y x² dx + ydy = 0 a linear?  2. Is y' = y+x / x a homogeneous Equation?

A: We have to check whether the given differential equations are linear and homogeneous or not. A…

Q: Find given that dt x² + y² = 2x+4y, x = 3 y = 1, and dy dt i dx dt

A: SOLUTION-

Q: dz Find given: dt xe2", x = t°, y = -1+ 6t dz dt Your answer should only involve the variable t

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Q: OBTAIN THE GENERAL SOLUTION 2. dx: t (1+e?) see" x dt 3. x dx - Ja - x² dy =0

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Q: C. Solve the following using Integrating Factor by Formulas. 1. 2y(x² – y + x)dx + (x² – 2y)dy = 0…

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Q: dy =f(x.y). y(x)-yo is dx By Picard's method, the third approximate solution of a. Y3 Yo+ b. None of…

A: We need to find the third approximate solution of dy/dx=f(x,y) , y(x0)=y0 by Picard's method.

Q: An integrating factor of (xy? – x?) dx + (3x?y² + x?y – 2x³ + y?)dy = 0 is A) ey B) ебу 1 C) 6y e D)…

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Q: 2y(x? — у + х)dx — (x2 — 2у) dy %3D 0

A: I think mistake in question inplace of -ve sign.

Q: Solve the Bernoulli equation for y by making the substitution u = y?. dy 5y + y'. dt Use the…

A: A differential equation is an equation that relates one or more functions and their derivatives…