If limi (2x+3) =5, find メ→ o for E:0.2.

Q: Q5. Use variation of parameters to solve the nonhomogeneous ODE. y" + 16y = sec³4x

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Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

A: I am attaching image so that you understand each and every step.

Q: (c) Given tanh (x) + tanh (y) = 1, show that, dy 1- y? dx 1- x2

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Q: If y = tan(4x + 1), determine using chain rule. dy dx

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Q: dy Find for ( In (t), at t = 8. dx (Give an exact answer Use symbolic notatio

A: Here x and y are given in terms of t. So to find derivative of y with respect x we have to find…

Q: The value of 'n' to approximate [x dx by taking h = 0.1 using Trapezoidal Rule is О а.2 O b. 5 О с.…

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Q: Given that y'= 3y - 100t and y(0) = 10, estimate y(1) using delta t= 0.01.

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Q: 03: Use chain rule to find dy/dx for the following 1. y = -sec u, u = x² + 7x

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: y to solve the following linear differe ] dy

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Q: when step Qal Evaluate the x²+2Xy + y? dy dx Size of x=0,2 and step size of y= 0.5

A: We have to solve ∫01∫02(x2+2xy+y2)dydx Given step size of x = 0.2 and step size of y = 0.5

Q: H-wlo Find the dliscontinnity point of &cz):

A: Since you have posted multiple questions. I am answering the first one. Please post the question…

Q: Hiw Solve y=Jx+y' for X=oco.2) 2 by given Xo=0,9o=0· Rung Kutta methood Por 0.0.E (first ordey)

A: Runga Kutta First order method is also known as Euler's Method.

Q: +00 1 1 : dx x[In(mx)]3 m+3 8

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Q: d?x +x = secy %3D dy2

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Q: dz Find- at t = n, if x=21sin' 12t + 170, z=19cos12t +190t . %D dx

A: The value of sin (npi) = 0 We will put t=pi in dz/dx

Q: 3) Find dz dy for z = e

A: Solution: As per given date   z=exy  For finding dz/dy , we assume that 'x' is a constant.

Q: For x-Arccos(31) y=Arctan(6t) find y when x=D0 0-1 0-2

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Q: cinxo ) 2X. dy dx Find for y= cos ( Inx + e

A: We have to find the derivative.

Q: E valauate the JJ x +2xy +ydy dx when step size of x-0.2 and step size of use the Trapazaidal Rale…

A: given I=∫01∫02x2+2xy+y2dydx with  h=0.2 let x0=0.2 , y0=0.5 let fx,y=x2+2xy+y2 substituting the…

Q: Find the general solution: dy = tanxtanydx %3D

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Q: lim (z,y) (1,1) 2x – ry – y 22 – y?

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Q: 1. a.) Use use the L’hospital rule lim(1+* dy b.) Use Devirative Rule to search dx from the equation…

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

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Q: Use Euler method to approximate the value of y(2.2), given               ay' - by = cx2 + dx   ,…

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Q: use the chain rule to find dy/dx for the followingy=sin^2 (3x-2)

A: Firstly, we introduce two new functions u(v) and v(x) as shown on board.

Q: For ey – In x=y2, find the value of so that & (y' – y') = 1 at y =0- O e e

A: we have to find

Q: If f(x) = – x Find: S",(f(x))² dx That is find S"(: ,(1 - x)?

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Q: Express æ = e-t, y = 2e2" in the form y = f(x) by eliminating the parameter y =

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Q: Suppose z is a function of x and y, and a? – y? = 2"e6y. Solve for dz dx

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Q: If y = 1+sin t ,x = cost at t = dy Find- dt by using Chain Rule, then choose the correct answer: a)…

A: Given curve is  y=1+sint  ,x=cost

Q: EA Solve the D.E. by Laplace Thans Ferm + 2y = 12 e given ycazo %3D

A: first we apply laplasa Transform both side then we solve

Q: On the back of this page (or on a new sheet of paper), use the equation )dx = limf(x) Ax n-00 i=1 to…

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Q: Find the G.S.of the DE. (ytu dy=D0

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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: Find f. (Use C for the constant of the first antiderivative, D for the con f'(t) = Vt - 6 cos(t)

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Q: Given: f(x,y) = x³y – y cosh x" Solve for D132

A: Given:                   fx,y=x3y-coshxy To find: The value of the partial derivative D132.

Q: If y = 1+ sin t ,x = cost at t = Findy by using Chain Rule, then choose the correct answer: dt

A: Given that: y=1+sintx=cost

Q: x dx using Sim | size 0.3 is

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Q: For y = y(x), solve the ODE y" + 2 sech? (x) ·y = 0, given that y, (x) = tanh(x) is a solution %3D

A: Given ODE is y''+2sech2(x)·y=0.       (1) one solution y1(x)=tanh(x) is known. Let other solution is…

Q: If x= Arctant, y=. 2ay" =17 when t=V2. 1+76, find the value of a if y' В © VE E -2/2

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Q: Use the chain rule to find dy/dx for th following (a) y= (3x^2 - 13)^3

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Q: S,Ly? e*ydydx 1-

A: Use Change of order of integration to solve given Integration.

Q: Given tanh(x)+ tanh (y) = 1, show that, dy 1- y? dx 1- x2

A: We can find the required answer as below

Q: If z = e* sin y, where x = s?t2 and y = s²t, by using Chain Rule find ôz/ðs and az/dt.

A: Let's find.

Q: If Xy+yd, find the value of dy 5- dx 2 at the point Coy-1)

A: Given problem is :

Q: Solve for the DE equation associated by the given function: у %3D Ае2* + Ве* + С. а.

A: the given solution of differential equation isy=Ae2x+Bex+C

Q: Find dy/dx in terms of x and y if ax^2-by^5=c^2. Assume that a,b, and c are all constants.

A: Given equation is-  ax^2- by^5= c^2

Q: Use the chain rule to find dy/dx for th following : y= (ax+b)^5

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Q: (c) Given tanh (x)+ tanh¯'(y) =1, show that, dy 1- y? dx 1- x2

A: The given function is: tanh-1(x)+tanh-1(y)=1

Q: Given that: 0 V40x – x² dx Find the value of m

A: From the given problem: I=∫04040x-x2dx So, we can also write as: ∫04040x-x2dx=∫040-x-202+400dx...1…