Given x = 22t + 47 and y 154t? + 144 da (i) dt dy (ii) dt dy (ii. dx (write the simplified answer)

Q: dy Find the General and Particular solution of dx 3y; y=3, when x=0

A: The differential equation is given as dydx = 3ydyy = 3dx∫dyy = 3∫dxlny = 3x+lnAlny-lnA = 3xlnyA =…

Q: dx dt dy dt х — 2у + t х — у + 2t

A: The given equation is dxdt=x-2y+tdydt=x-y+2t This equation can be rewritten as x'=x-2y+t t=x'-x+2y…

Q: 2) dy x+3y dx 2x

A: We will solve the problem

Q: dy dx\, Given that x = t e and y = 1² e“ +1¸ Find = - 1

A: We have to find derivative at that point

Q: dy y3 , У (0) : 1 dx 1– 2xy2

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Q: find dy/dx in terms of x and y if (x-a)^4+y^4=a^4. Assume "a" is a constant dy/dx=?

A: Given: (x-a)^4+y^4=a^4

Q: If y = u and u =3x +3, find dy when x= 1. dx dy (Simplify your answer.) dx Ix 1

A: The solution is given as

Q: Given x = 4 In(t) and y = 16 t² then find dy dx d²y dx?

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Q: Given x = 2t - 35 and y = 4 sin t dy (i) dx dy (ii) dx2

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Q: Find the solution. dy -+y= dx 1+e y = ce+e "*In(1+e") B y = ce"+e*In (1+ e*) y = ce -e *In(1-e") ye'…

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Q: (2? + dy = 0 + In y) dx +

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Q: Given the equation dy = 3x2 +1 with y (1) = 2 %3D dx Estimate y(2) by Euler's Method using h = 0.5…

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Q: The general solution of V – 2x)dx+(2xy+ 1)dy=0 is?

A: (y2-2x)dx+(2xy+1)dy=0y2dx-2xdx+2xydy+dy=0y2dx+2xydy-2xdx+dy=0d(xy2)-2xdx+dy=0Now integrate both…

Q: Differentiate implicitly to find dy/dx. – y2 = 38 x2 + y2 dy = ? dx

A: Use the basic concept of the differentiation and simplify.

Q: If 3x2 +2xy +y² = 2, then the value of dy at x=1 is dx

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Q: NOTE: Enter the exact answer. r3-y 5y dx dy

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Q: rt%3Dr/6 t cos(2t) dt t=D0

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Q: (b) x²e3 dx (d) arctan 4t dt

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Q: Find the general solution of the equation тx dy %3D пу dx

A: see calculation below

Q: dy d²y — 4х — + бу 3D 4х — 3 dx² dx

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Q: dy is equal to- dx If y = !, then the value of +3 V1 +y* V1+x

A: Introduction :

Q: Solve for the solution for the equation: (x² + 3xy)dx + (x² + 4y) dy = 0 with the condition of y(2)…

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Q: dy x2 (b) Find the general solution to the DE cos? y dx

A: As per our guidelines only one question can be solved. Solution for "b" is given below in the next…

Q: Solve the equation dy/dx=1-y , given y(0)=0 using modified Euler’s method and find y at x=0.1 and…

A: Given differential equation is, dydx=1-y, y(0)=0. To find the solve the differential equation using…

Q: Find the general solution of (x +1)3d²y dx? 1TE + 3(x + 1)² + (x+ 1)y = 6 ln(x +1). dy dx

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Q: 3 2 Find for y = dt, where x> 9t+2 dx dx

A: The given function is y=∫0x39t+2dt. Let u=9t+2. Then, du=9 dt. The upper limit will be 9x+2 and the…

Q: dy + y =0 dメ 0 2) dx?

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Q: Finally, we substitute for u to write the answer in terms of x. Use C for the constant of…

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Q: Zy dx = (x?-1)L dx-dy) %3D

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Q: Use Picard’s Method with 3 iterations to solve for y(0.1) and y(0.2), the equation dy/dx = x2+y2;…

A: Picard method: Consider the initial value problem, dydx=fx, y, yx0=y0 Then  yn+1=y0+∫x0xfx,yndx…

Q: Find the solution of the this differantial equation. extan(y)dx + [(ex)/(x-1)]dy = 0

A: Hair we use the variable separable method to solve this equation.

Q: Find the solution of dy X. +y.Inx y.lny dx Show all your calculations.

A: Given equation is as below :

Q: dy Solve the initial – value problem: = y² given that f(0) = -1 dx %3D

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Q: Solve using Bernoulli's Equation 1. x^2(dy/dx)+y^2=xy

A: We have to solve the given equation

Q: 30. cos(r + y?) dx dy 32. x²+ y² dx dy 2 y

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Q: Solve the DE by Bernoulli's Equation 3 1.6 y² dx - x (2 x³+ y) dy = 0

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Q: For which value of a the equation dz dy dx =2 -1 does hold?

A: The constant rule of integration and the power rule of integration are given by and, respectively,…

Q: dy 1+y3 Determine the solution for the given DE: + = 0 dx xy?(1+x²)

A: Proceed as shown below

Q: Hello there, can I please get this question answered? Thank you!

A: Given:

Q: If x = 5t +4 and y = 3t-7 , then find dy at t = 2. dx а. 1 O b. 2

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Q: Solve the Euler equation 2r dy 2.x dx? -3r given that y(1) =1 and y'(1) = 2. +3y 0 dx jntaios

A: To solve given differential equation first we write the auxiliary equation and find the roots and…

Q: d’y dx? Find the general solution for +10 -+25y = 0. dx

A: For the second order homogeneous differential equations of the form ad2ydx2+bdydx+cy=0 , the general…

Q: For which value of a the equation dz dy dx =2 does hold?

A: as per guidelines we only solve one question at a time if you want to know the answer of all please…

Q: Using dy = 3 dx and dx = 0.03, what is dy when x = 2? 2V3X – 2 dy (Write as an exact decimal.) %D

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Q: sec?y dx? – csc²x dy? = 0

A: The given differential equation is sec2 y dx2-csc2 x dy2=0, which can be simplified as follows: sec2…

Q: Solve xy( 1 + x y? ) = 1 by using Bernoulli's equation. %3D dx

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Q: For the equation, 2y(x^2 - y + x)dx + (x^2 - 2y)dy = 0, what is the integrating factor?

A: