df df-1 (c) Evaluate df-1 at x = a'and dx at x = f(a) to show that at these points dx dx dx) x+24 1. f(x): 1 a = ー x-=の %3D 1-x' (-)入

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A: Given ∫23∫-14∫104x2yz-z44dz dy dx ∫23∫-14∫104x2yz-z44dz dy dx=∫23∫-14∫104x2yz dz dy dx -…

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Q: 3.b) Evaluate the DE * 3x(xy – 2) dx + (x³ + 2y)dy = 0

A: Given that: 3x(xy-2)dx+(x3+2y)dy=0

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A: The given equation is

Q: Q1/ Evaluate So (x² + 3y²) dy dx using Simpson's 1/3 rule in x-axis and Simpson's 3/8 rule in y axis

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Q: 1. Classify the D.E. 2xe dx + (x²e + 1)dy 0.

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

Q: what is dy/dx?

A:

Q: 1. S (x¹+3x²+1) dx 2. f(x³ + x² + x−¹)dx p³ +p²+p+1 dp 3. p3 √ 2² (√z + √z-1) dz 8x³+27 -dx 2x+3 5.…

A: The objective of the question is evaluate the anti-derivative.

Q: Z4 e: 2₁₁ (4x²yz - ) dz dy dx 1 4

A:

Q: I. FIND THE GENERAL SOLUTION OF THE FOI dy dy = xy + 3x - 3x dx 1. dx

A: As per our guidelines we are supposed to answer only one question

Q: find particular solution of (16x+5y)dx+(3x+y)dy=0. If the curve to pass thru the point (1,-3)

A: Given: 16x+5ydx=-3x+ydydydx=-16x+5y3x+y               It is a homogenous differential equation.…

Q: If y=x^2 e^2x then dy/dx is equal to

A: we have,y=x2e2xdifferentiating both the sides w.r.t. xusing product rule,we…

Q: If x =t-1+5 and y 6+t-2 then dy at t = dx is

A: topic - derivatives answer is 4

Q: If y = e Oe3 Oe 3x X² O 2e3 O 3e³ then dy dx at x = 1 is

A: To find derivative of given function at x=1

Q: Find dy/dx at the given point without first solving for y. x2 + 4xy + 23 = 0 at (1, −6)

A:

Q: 3. Determine the Particular solution of this equation In terms ofY (xy2)dx + e*dy 0, as x → 0, y ==

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Q: 17. (Vx-x)dx (1-x²) dr 18. 19 o. Sy² dy 20.

A: Given problems:-

Q: SíS(x² + y²) dx dy 0.

A: To evaluate the given iterated integral.

Q: Show that if you differentiate both sides of x 2 + 2y 3 = 6, the result is 2x + 6y2 (dy/dx)= 0. Then…

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Q: Find y in terms of x. dy dx 5x 3/4, curve passes through (1, 10) A) y =- 7/4 א. -714. 5 By = 5x 1/4…

A: The given differential equation is dydx=5x-34. It is given that the curve passes through the point…

Q: 0. ° (x? + x) dx -2

A:

Q: b. y = cosh(arctan 3x) C. y = 4a/ cosh a d²y d. for x = 4v2t2 + a, y = a² – t² dx2 %3| -

A: Given functions are  b) y=cosh(arctan3x) c) y=4acosha d) d2ydx2 for x=42t2+a , y=a2-t2

Q: I. Find the general solution of the following: dy 2x 1.- dx y dy 2. xy dx 3. dy = (6e3x+ 1)dx

A: We have to find the general solution.     According to our guidelines we can do only one question so…

Q: 2. Find an expression for dy/dx on the curve x In(y) + x³ – 2y = 6.

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Q: 5) If y- x-2x and at ts V2 Find dy

A: To find dy/dt at t=sqrt(2)

Q: Find dy/dx for y = 3l(sin-(e-3**)12 dy 3(sin"(e-*)* In3 2(sin-"(e-3x*)- dx 1(-6х) V1-e-6x2

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Q: Show that if you differentiate both sides of xy +4x + 2y = 1, the re- sult is (x + 2) + y +4 = 0.…

A: we have to show that the differentiation of xy+4x+2y=1 will result in (x+2)dydx+y+4=0 and then we…

Q: Find the differential dy. y = (x+4)/(x-4)

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Q: -2.1 1- e* Use Simpson's rule to approximate -dx. x² + 2x – 1 1.2

A: This is a problem of numerical Integration.

Q: А. dy (1,1) = 1 dx dy (1,1) = -1 dx B.

A:

Q: The general solution of (y-1)dx −2(x+y+1)dy=0 by CL2V is

A:

Q: Find the general solution by means of separation of variables if: dy = xy -x dx

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Q: Find the particular solution from y(9x-2y)dx-x(6x-y)dy=0  when x=1/3 and y=5/2.

A:

Q: I. Find the general solution of the following: 2 dy = -2x + 3x -2x = 3e dx (x²+5)dx- (2y - 1)dy = 0…

A:

Q: 4x − 5y + 3)dx − (2x − 3y − 1)dy = 0 how solve this problem?

A:

Q: dy dy = xy + 3x – 3x dx dx

A: The given differential equation is: dydx-x2dydx=xy+3x-3x3Therefore:dydx=xy+3x1-x21-x2

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A: We know that general derivative of d(xn)/dx is nxn-1. And derivative of d(sinx)/dx = cosx  d(lnx)/dx…

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A:

Q: 5. Let y=(f(x)+5x^2)^4 and suppose f(−1)=−4 and dy/dx=3 when x=−1. Find f'(−1).

A: Given , y = (f(x) + 5x2)4 and also given that ,f-1) = f , dydx =3 when x=-1 , we have to find f'(-1)

Q: find the PS of (16x+5y)dx +(3x+y)dy= 0. if the curve to pass thru the point (1,-3

A: 16x+5ydx+3x+ydy=0 -1equation 1 can be written as

Q: Obtain the general solution to the equation. dy 4. x+ 2y = x-3 dx

A:

Q: 2) Solve the following problems a) x (y- 1) dx - y lx²- 1) dy = 0 b) Sxy' = y=xy lyl-1)=1 %3D

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Q: For (3x – 5x) V2x+1 find dy/dx at x-0

A:

Q: 3.) S, t°(1+ t*y°dt 4.) (x²-5x)e*dx 5.) S(4x²-7)dx/2x+3

A:

Q: I sin 2 dy dx (x² – y) dy dx 5. 6. x? – y² dy dx 8. L ellyt dx dy 7.

A:

Q: d) Obtain the particular solution of (2x– 3y+4)dx +3(x-1)dy =0; when x=-1, y = 2

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Q: if y=(x+1/x)/(2x-3) the dy/dx will be

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Q: -1 x-x2 dx -8 2도 1423 1521 22 20 Option 1 Option 2 1425 1523 22 20 OOption 3 Option 4 None of the…

A: Given problem:-

Q: 4. If x = 1+1 & y==1-t² then dy - at t =1 is dx а) 1 b) 2 c) -1 d) - 2

A: Value of dy/dx at t=1 is