dy Use dsolve to solve dt 3D 5у — 5ty³

Q: 2x Ex FIND THE DERIVATI VES %3D

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Q: ds-(s + et)dt=0 (find DE,prove if exact or not)

A: dsdt=s+et  It can be solve by integrating factor method I.F =e∫1dt =et solution of DE is…

Q: If the substitution u = x/2 is made, the integral 1-(플)2 dx = %3D -

A: Let's integrate.

Q: d²y dy dt + 81y = 0, y(0) = 9, y' (0) = 3 + 18- %3D %3D dt?

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Q: r2 dt V4 + t?

A: The given integral is: I=∫02dt4+t2

Q: find Neumann senies for The solution of the integraL equation.- O go) - f6) +dSé g(4) dt %3D

A: Solution 1: Given integral equation is g(s)=f(s)+λ∫0ses-tg(t)dt Here k(s,t)=es-t Let k1(s,t)=k(s,t)…

Q: What is §3dx, §5du and §e^u dt? Those are integrals

A: a) We factor out 3, then integrate. c=integrating constant

Q: By using the substitution method, show that for any positive numbers x and y ry 1 dt = Sdt

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Q: Evaluate the integral: ft² ns te" du ds dt

A: Let's evaluate given integral.

Q: Evaluate the integral. (2 + 2y)? dy

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Q: Provide an appropriate response. If xy + x = 12 and dx/dt = -3, then what is dy/dt when x = 2 and y…

A: We will find the value of dy/dt with the help of the given data x=2 ,y=5 and dX/dt=-3 as following.

Q: Evaluate the integral 20 | by making the appropriate substitution: u = 5 – 2 (2³ – 2)® dx %3D -

A: Evaluate the integrals

Q: dy Exercise: find O If y= Vu ua Sinx y= -Secu %3D

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Q: integrate by parts t7 sin⁡(2t4 )dt

A: We have given indefinite integration with respect to x. While solving the indefinite integral, we…

Q: Evaluate tne following double integral ! VI- 2 (2 + y)* dyd.r. -1 0

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Q: dy dt 1. y=V(3t2 - 2t + 1)(t2 – 1), 12/07/2021 18: 54

A: Given that       y = √(3t2-2t+1)(t2-1)  Here we have to find dy/dt .

Q: Apply Green's Theoren to evaluate the integral. C6x+y) dx + (3xy"+4y) dy ter

A: Given integration is ∮c(6x+y3)dx+(3xy2+4y)dy C : Any simple curve in the plane for which Green's…

Q: Evnlunte: (а) (- xy) dydx (b) dr(x-) dy, where y, = Va? - x?

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Q: Estimate the value of the integral 4- x²y2 dA, S = {(x,y)| x² + y? 0} |

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Q: Evaluate the double integral : 9. dy dx 0, 22

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Q: dt2 d²y e. ++ 4y = 8t – 10, y(0) = 1, y'(0) = 7 %3D %3D %3D

A: As you post multiple questions According to the guideline I only solve the first problem. Please…

Q: raluate the double integral : (x + 2y – 2) dy da

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Q: Evaluate the integral. 7y° V8- 7y* dy y18-7y* dy =

A: Given integral is We will evaluate the integral by using following substitution

Q: Use the substitution formula to evaluate the integral. fin-√3/22 c2x dx 1 + e4x 28) 0

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Q: Find rsint V1+ u+du) dt. dx2 Jo

A: We have to use the formula  Here  We write the second derivative as two derivatives and use f(t)…

Q: Evaluate the iterated integral. (3x - 2y) dy dx 1 Jo

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Q: Find at x = 4 if y = 4x² - 2 and dt da dt Question Help: Video Submit Question dt = - 3.

A: We are asked to find the derivatives.

Q: Evaluate the integral dx (4x + 14) by making the appropriate substitution: u = dæ (4x + 14)* Submit…

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Q: Use the local linear approximation of (1 – x)2º at xo O to estimate (0.99)2º. %3D

A: The linear approximation of f(x) at x0 is given by L(x) = f(x0) + f'(x0) (x-x0)

Q: d²y csinx Find if t Vt2 + 5 dt + sinx = y – x secx dx2

A: We will first find the first order derivatives using Newton-Leibnitiz theorem. The , we will find…

Q: Consider the following. dz 4z + 2 1 Find a substitution to rewrite the integrand as du. 4u du = dz

A: Given : ∫dz4z + 2

Q: @ Consider the DE, dx %3D dt x (2t -7) What meho can be uoed

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

Q: dy e, solve the IVP = 40 dt 5y y(0) = 10. - %3D 100-4t cag

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Q: Evaluate the integral ex 2e-2x - 3e2x | Arcsin V6e2x 2 A V3 +C ®Arcsin l V3e2x +C B © 2/2e-2x - 3e2x…

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Q: Evaluate the integral. e sec²(8x) dx %3D +C

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Q: Evaluate the line integral. L(4x – 8y) ds C:x + y = 100 (4x - 8y) ds = i |

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Q: Sv? – 1),/y dy

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: I = 1- 6x?y dx dy.

A: In double integration, we start integrating from the inner part with respect to the inner variable.…

Q: Assume that y= 5x and de/dt = 2. Find dy/dt. Select one: 10 O 5 O 2 1

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Q: integrate t dt/(1-ct) where c = const.

A: Solved below

Q: dz dt 3x – 2y fip dt 9x - 3y %3D z(0) = 1 %3D

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Q: dy(t)25dy(t) + dt + 2y(t) = %3D dt2

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Q: Evaluate the integral. 4VE e dt Vt 4VE e dt =

A: This is case of integration by substitution where we look for an derivative in the integrand.

Q: Show that {zn}nEN is Cauchy, where z, = sint dt. 1+t

A: Sol

Q: Approximate the integral | dx using 4 trapezoids .2 1

A: Introduction: The formula for the trapezoidal rule is given by, ∫aby(x)dx=h2y0+yn+2(y1+y2+...+yn-1)

Q: dy – 2ty = –31²e? dt - and the condition v(

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Q: Evaluate the integral dz dy dr. -2 Jo 5-722-7y2 32

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Q: Determine the solution of y dt + (2yt + I) dy -Ogiven that given that y (-1) = Q

A: 2. We need to determine the solution of the differential…

Q: By using homogeneous meth od , solve dy %3D

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