Find k so that dx = ke" + C.

Q: Given that y=e is a solulion to y" + 4y'- ky = 0 . What is the value of k?

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Q: Then show that Their G.M is equal to the A.M and H.M lie e=dAXH - CM of their

A: First we determine A.M, G.M and H.M of positive numbers a and b.

Q: d (arccot(x)) -1 Be sure to provide a written justification for 5. Prove your work. dx 1+ x2

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

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Q: Evaluate L e* dx dy by using trapezoidal and Simpson's rules.

A: Given that, ∫02∫01ex+ydxdy By trapezoidal rule, ∫abf(x)dx≈h2f(a)+2fa+b2+f(b) where h=b-an…

Q: if y= e-e-X dy %3D Show that %3D e* te*

A: We have to prove this equation

Q: Q2. Show that dx ax + by di dy = cx + dy di can be written as + yx = 0

A: The given system of differential equation is. dxdt=ax+by                     ......1dydt=cx+dy…

Q: Exercise: Answer the following by finding dy/dx. 5sin-1 # – cosh x (a) y = Vsec4 x + In 7 4 (b) + In…

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Q: (Note: This is a f(x) of Hyperbolic) e¯* + e* dx о ех — е х

A: We have to solve

Q: find all soutions of sec? (x)=VZ on the intorrel Os BK27T

A: NOTE: Refresh your page if you can't see any equations. . take square root on both sides

Q: Evaluate e* dx dy by using trapezoidal and Simpson's rules.

A: Hello. Since your question has multiple parts, we will solve the first integral by first method for…

Q: After using z = X - y as substitution, the DE (x-y)^2 * dy/dx = a^2 (a is constant) transforms to…

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Q: - If x=sect and y = tan t, evaluate at t of the following: 4. dy (a) dx d y (b) dx?

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Q: Evaluate sczxay) dx^ (x+ 3y) dy along the poth C: ure on y =1-3 from l0,)) to Cl,0)

A: Line integral problem......

Q: Reduce the given DE into Bernoulli's equation: dy_y 2x* y-4 - dx 3.

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Q: Find he value of ds /dy at u = 2 if s = t2 + 5t and t (u² + 2u)3 du %3D

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Q: Given y = ecos" a, at x = a dy > dx

A: Given that  y=e^(cos^3x)  To find the dy/dx at x=π/2

Q: Consider the figure below. uestion 1 T. 2x W Зх - 5 Previous

A: Given TW= 2x, 3x-5

Q: Find e + Uy, Given that u(x,y) tan(x+11Xy+11y") .t/ - *א- w

A: Given ux,y=tanx+11x2y2+11y411-x2-y2

Q: Find the value of ds/du at u = 2 if s = t^2 + 5t and t = (u2 + 2u)^(1/3).

A: Find ds/dt from s=t^2+5t

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: nis is an exact DE. * 3x+ Qy? ) dx t (Axy t ly') dy = 0 O True O False

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Q: Given: y = sqrt(u)  ,  u = 2x2 + 3x + 4 Determine dy/dx at x = -3 a) Using Leibniz Chain Rule b) By…

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Q: Given x 13 In(t) and y = 169 t2 then find %3D dy dx dy dæ?

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Q: dy 3) Determine the of : In (ху?) %3D х у dx

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Q: Q4/is that, the Sulutton to the differentiel equation dy-tX+4. is it's

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Q: dy IS let y = (cos r)m " then de sin z

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Q: dy %3D xp

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Q: Use Green's Theorem to evaluate ya dz – x dy where C is shown below. Left Half of (0,5) x*+y = 25

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Q: If y =Aex +Be™ d'y -(m+n) dy. Show that + mny = 0 dx

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Q: Without eliminating the parameter, find d²y at t = 2 1 x = 1

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Q: then show that dz+z = % dy e te

A: Given:z=ex+yex+eyDifferentiation formula:ddxuv=v.dudx-u.dvdxv2

Q: Given z = 15 In(t) and y =225 t then find dy da dy da?

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

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Q: Find dy du dy and when y and u are defined as follows. du dx dx y = 3u² + 6 and _u = x² + 2

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Q: Evaluate SSS 12z dV E where E is enclosed by z = x? + y? and z = 1

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Q: Given that y=ax , find dy/dx

A: To find the derivative of the given function

Q: dy Given that y = In 9x, find dz dy

A: Use derivative rules to find dy/dx

Q: t DR) dende Dartine dövßes e te than show that Deo) X DR1) to DG20). o is atoxphic

A: To show D20×D21 is isomorphic to D420: Define a map f:D20×D21→D420 by fa,b=a×b a×b∈D420: Suppose a…

Q: s zy dydz こミ0

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Q: Given z 15 In(t) and y= 225 t then find dy da dy dr?

A: Given that: x=15ln ty=225 t2

Q: Sv? – 1),/y dy

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

Q: Exercise: Answer the following by finding dy/dx. 5sin-lr cosh x (a) y = Vsect x + In 7 4 (b) + In y…

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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 y= V (x-1), find dy (Use rules, not a de finition ) Xp

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Q: Differentiate e w repect to X. expression (x2+y)" (use D fur dy)

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Q: If the substitution U = Jx is used, then S dx is equi valent to ?

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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: If we have to check the DE (5-8y+4xy)dx = (x+2)²dy for Exact then My

A: M dx + N dy =0