Soluie the giren îuitial-value problem dx =5 smwt; x6) =0; dx tox に dt

Q: dy at the poin dx

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Q: Solve the DE: dy sin ) + dx II

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Q: Evaluate dy/dx at x = 2.5, correct to 3 significant figures, given y= (2x^2+3)/In 2x

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Q: dy sin x Ify= et dx

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Q: (x– x'ye" )dy – dx = 0

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Q: (8) dx Compared to I dx x In|x| Conterges or Diverges

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Q: In the case of a double integration, what changes if we change the order of integration? (Ex:…

A: we know the limits of integration the dx dy order and need to determine the limits of integration…

Q: 2(y+1) dy t 2) 2(у + 1)4 dx x+1

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Q: y = [cosh(2x)]ot*( 1 cot-1 3 Vx

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Q: Find dy/dx and d2y/dx2 without eliminating the parameter. x=1-t^(2), y=1+t

A: x=1-t2,  y=1+t Differentiating with respect to t, we get dxdt=0-2t  &  dydt=0+1⇒dxdt=-2t  &…

Q: dy = 9 +y osx dx

A: Given

Q: to determine the approximate value of v(1+x³)dx

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Q: e*dx cln 1 Calculate Jin 0.5 V1-ezx" (b)

A: We will solve this integral via substitution:

Q: Inx Iny mz dx dy dz

A: Given integration is  I=∫1e∫1e∫1elnxlnylnz dx dy dz=∫1e∫1e∫1elnx dxlnylnz dy dz…

Q: SOLVE THE FIRST ORDER DE. dy – yln(yecosx)dx = y sinx dx

A: dy-yln(yecosx)dx=ysinxdx

Q: 5 dx, correct +2x²) Problem 19. Evaluate (3 to 4 decimal places

A: ∫0152x2+3dxSubstitute u=2x3→dudx=23→dx=32du=∫532(3u2+3)duSimplify:=523∫1u2+1duWe know that…

Q: Find dy/dx. x = t/(9+t), y = (9+t)^(1/2) dy/dx = ?

A: We have to use the parametric form of differentiation . In parametric form of differentiation , we…

Q: EXAM Q1-If x= cot-1 VE, y =,-. find dy d2y dx' dx2 at t = 2.

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Q: Find dy/dxin terms of x and y if (x−a)^4+y^4=a^4. Assume that a is a constant. dy/dx=   implicit…

A: (x−a)4 +y4 =a4 a is a constant. dy/dx = ?

Q: ) L -dx (x² + 1)²(x² + 2x + 2)` sen? t dt, for 0 <b< a. a+b cost

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Q: dy Find by implicit differentiation. dx 8x? = 5 - ey dy %D dx (Type an exact answer.)

A: Consider  8x2=5-ey

Q: 23. Lx? sin y dy dx

A: Given: ∫-11∫0πx2sinydydx for finding given integral we integrate one by one

Q: y_x + y х х — 1 dx

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Q: Without integrating, explain why: S, ?)°dx = o x(1+ x* -2

A: To show:     ∫-22x1+x22dx = 0 (without integrating)

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

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

Q: S sin Vat dt

A: Let the given integral be: I=∫sinat dt

Q: Solve the inital value problem from the differentail equation: dy/dx = 1+ y       where y(0) = 1

A: Given: Initial value problem. dy/dx = 1+ y       where y(0) = 1

Q: Evaluate xy dy dx ?

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Q: Solve: dy + y² = ty dt

A: A differential equation is said to be Bernoulli's equation if the equation is of the form…

Q: 4. Bernoulli's Equation 3dy – 4xy dx = 3x²y*e=2x² dx Зdу — 4xу dx

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Q: 1. dx Evaluate 0, et +e-*

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Q: Use Bernoulli's Equation dy/dx+ycotx=1

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Q: Differentiate. Inx y= 3 dy dx

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Q: LL y e* dz dx dy -Inx

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Q: (5x )cos( - Jax + S, (5x – 15)cos( 1.5 a 1.5 1.5 dx

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Q: Solve the following Exact DE using Method of Grouping. 3) () dx + () dy = 0 X-X y

A: Given:          2x-1ydx+x-x2y2dy=0     This is in the form of   Mx,ydx+Nx,ydy=0    where Mx,y=2x-1y…

Q: From the figure formed in integrating -dx, what is the term or value that is adjacent to the angle…

A: Given:    ∫x2-3xdx

Q: Find dy/dx at the given point without first solving for y. xy2 = 343 at (7, 7) dy %3D dx

A: Given query is to find the derivative of the expression.

Q: t seel dx

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Q: /hat is the value of dx at the point (1,0) if y = In(x² +y²)?

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Q: Solve the initial value problem. dy ху?- сosrsinx а. у (0) %3D 2 dx (1- x?)

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Q: Зх-1 dx; J x²+10x+28 Зх— 1 Sa :dx (x + 5)² + 25' Зх — 1 -dx Ja+ 1)² + 1 Option 3 Option 1 Зх - 1 dx…

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Q: | (In x)? dx. 1. Use integration by parts.

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Q: 3 S S t² etu du dt

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Q: Show that d/dx(ln kx) = d/dx(ln x), where x &gt; 0 and k is a positivereal number

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Q: Find dy/dx at the given point without first solving for y x2 + 3xy + 11 = 0 at (1, –4) %3D dx II

A: Given: The curve is x2+3xy+11=0 and the point is  1,-4. The objective is to find dydx at the given…

Q: I = Si S (x² + y³) dy dx.

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Q: Determine the solution to this DE: * dy t By 2 dx

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