What is the characteristic equation for dy 2. dt d²y y +2+e' sin 3t dt 2

Q: the general solution of the DE (cosxcosy+2x)dx-(sinxsiny+2y)dy=0 is

A: The differential equation M (x, y) dx + N (x, y) dy = 0 is exact if and only if  ∂M∂y=∂N∂x.   The…

Q: dw Find the value of- dt at the point (1, In 2 ,0) on the curve x = cos t ,y= sin t, 0 <t< 2n where…

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Q: Suppose that a point is moving along the path xy= 1 so that dy/dt=4. Find dx/dt when x=3.  dx/dt=?

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Q: Which of these gives an integrating factor for dy 2ty = 3t + 1 dt -

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Q: d²x dx + 2 * + 5x = e-t sin t; dt [ = x(0) = 0 x'(0) = 1 %3D dt2

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Q: A. Integration by parts o (3t + t*) sin(2t) dt

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

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

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Q: dy -y ze°Cos(E) dt y le) =0 1+らine

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Q: Find the differential dy. 1- 5x y = 4 dy = dx

A: Given that y = (1 - 5x)/4 Find derivative of this y. Here i attached solution of this question.

Q: dy dt 1 Find if 4y°t + t°y = 2 and dx dx cos t dy dx

A: To find dydx here we need to use both chain rule and product rule of differentiation.

Q: dw "(1),y = sin (1),-: 2) w=+ x= cos at =3 Ans. -1 dt

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Q: 一3十 Sin zt dt

A: We have to use first shifting property and Laplace transform of integration property to Laplace…

Q: Find dy/dt. y= cos ~ 10t + 11)

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Q: Find the differential dy. y = ex/2   dy=

A: Here the given expression is y = ex/2. Apply the chain rule:

Q: dy Find for y = cos (8at + 1). dt dy dt

A: We have to find out dy/dt for given y

Q: The solution of the differential equation using dy + 6y = 7e-3t is dt Laplace transform „given that…

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Q: Find the differential dy of the function y = Provide your answer below: dy = dx 5x4 + 4 4x + 3

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Q: dx + 2x = dt dy + 10 cos t, dt ay + 2y = 4e-2t – dt 业 da if x = dt rstem

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Q: find dy/dt Y= (1+cos4t)^5

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Q: Find the Wronskian for the differential equatio: dy dx2 fip dx 3 10y = 0

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Q: Solve the DE Ssinx siny dx + cosx cosy dy = 0 by separation of variables. sin y A cos X B sinx cosy…

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Q: What is the integrating factor of the non- exact DE (4ху+ 3у?-х)dx+x\x+2y)dy %3D0 ?

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Q: 5. Solve dy+dy =5 with y"(0) = 0, y'(0) = 2, dt dt У (0) %3D0

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Q: Find the differential dy of the given function. y = Invs - x dy =

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Q: *Yx = cos°(t), y = sin (1),z =, dw = 1 dt w =-+2,x= z Z ==, at t = 3 Ans. t=3

A: Given query is to find derivative of w with respect to t.

Q: dy 4. y dx ;y(1) = 3 x(х+1)

A: In this question , Firstly we can integrate on both sides and solve the integral. After that we can…

Q: Find dy/dt. 13) y - cos (πt - 19) 14) y = 4t(5t + 2)4

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Q: Use the method of Example 4 to compute dy/dx p at P = (2, 1) on the curve y^2x^3 + y3^x^4 −…

A: we can solve by this implicit differentiation, so,

Q: (b) [(2t – n)0"dt ja- (a) x In x dx (c) 2x sin x dx

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Q: A ) Find ſ cos 5t dt dy B) If y = x² +; , x= 2t -5 then find dt

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Q: Find the differential dy of the given function. y = V 3 - x2 dy =

A: Find derivative

Q: dy = (x – 2)e-2y dx einitial condition y(2) = In(2).

A: Explanation and solution is given below.....

Q: 8. When reduced to a linear DE of order one in z, bernoulli' equation dy/dx +y (1/x) =3x2y2

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Q: Find the differential dy of the function y Provide your answer below: dy= dx = 5x4 + 4 4x + 3

A: y=5x4+44x+3Differentiate w.r.t xdydx=4x+320x3-5x4+444x+32

Q: dx-(it 2x tany) dy-0

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Q: Find dy if y = In* +1 7 -t dy dt

A: Derivative is below

Q: 3. Find dy/dx of the followings: (а) у | V2 + cos³ t dt 2. •7x2 (Ъ) у V2 + cos³ t dt 2 (c) Y 1 dt t2…

A: using fundamental theorem of calculus part 1 ddx(∫abf(t)dt)=f(b)ddx(b)-f(a)ddx(a)

Q: dy %3D 3 e*y* dx +

A: Givendydx+y3=exy4To Find:Solution of a given Bernoulli's equation

Q: Find the differential of the function y = In(S - 2x) 2dx dy = (5-2x) dy = (5 – 2x )dx -2 (5-2x)dx…

A: Given : The function y = ln(s - 2x).   To find the differential of the function y = ln(s - 2x).

Q: Find the particular solution of this DE: dt = ev-t(1+t²) sec y; y(0) = 0 %3D

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Q: Find the general solution to: dy d dx dy 1 dy Cos x + sin 2x dx x + 4 dx

A: d). Given differential equation is dydx=cosx+sin2x. Re-writing the given differential equation.…

Q: Find the particular solution if dy/dt=sin(t) and y(2)=2.

A: Topic:- application of integration

Q: 4 cos x Let y = [, (2t + 1) (t + 8t)'/3 dt. Find dy/dx.

A: We will find out the required derivative for given function.

Q: By (d) dy 2- = 3t + 2, y(0) = y'(0) = 0. dt By +4 dy + 20y = -3 sin 2t, y(0) = y'(0) = 0. (e) dr² dt…

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Q: dr Suppose dx dt dy 4, = 3. Find given that r = dt dt x = 8 y = 2 Write your answer in exact form,…

A: Topic = Derivative

Q: dy dx 2 at x = 5 if y = 4x? + 5 and dt = 4. Find %3D dt

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Q: dy dt 1 Find dx if 2y°t + t°y = 4 and d.x Cos t

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