F. Solve the following by Substitution Method. 1. y(x tanx + In y)dx + tanx dy = 0

Q: dy for y dx defined implicitly by the equation tan(x²y*) = 3x + y? 1. Find

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Q: dy Find the General and Particular solution of = 8 sin 4x ; y = 6 when x = 0 dx

A: Given that : The differentiable equation dydx = 8 sin 4x . y = 6 when x = 0.

Q: 1 dy 3. С + 2y = sin x when y(r) dx

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Q: Q.5/ A) Find dx for the following equation y = In(x2 + 4) – x tan-() %3D

A: Given equation is y=lnx2+4−xtan−1x2 We have to find dydx. Used Formula:- ddxlnx=1x ddxtan−1x=11+x2…

Q: Solve the following equation for the given conditions y(0) = -1,y'(1) = 2 d²y dy + 4 dx :+ 4y = sin…

A: Given differential equation is d2ydx2+4dydx+4y=sin2x+cos2x      (1) with y(0)=-1, y'(1)=2 Auxiliary…

Q: Q3. Solve the following DEs. 1. y dx 1 dy 1 Iny = sinx (In y)?

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Q: Q1: Find dy/dx for the following functions (solve four only):- (1)5Y + 5*y = In sin-1 e* (2) y =…

A: 1)      5y+5xy=lnsin-1exDifferentiate partially both…

Q: (x tan x + In y )dx tan xdy + :0 y

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Q: F. Solve the following by Substitution Method. 1. y(x tanx + In y)dx + tanx dy = 0 dy %3D

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Q: Answer the following neatly and completely. Find dy/dx. 1.y = sin(x²e3*) 2.y = In (tan x?) .xcos y –…

A: Chain Rule of Differentiation : If we have y=f(u) and u=g(x) then dydx = dydu·dudx

Q: Solve the following DE: [2x+ ycos(xy)] dx+ x cos(xy) dy = 0

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Q: dz Find dy x? sin(2y – 5z) =1+y cos(6za)

A: The given equation is: x2sin(2y-5z)=1+ycos(6zx) To find ∂z∂y, differentiate above equation w.r.t. y…

Q: dy 29 + y tan x: dx 1 (4x + 5)? y³ cos x

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Q: Solve the following IVP. You may leave your answer implicit in y. dy = 0, (2.x+y³ sec² (x)+ (1+ 3y²…

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Q: c fx) = at (4, 2) 3x – 4 d y=x In x at (0, 1) sin3x at y =- x? 4 e T 2

A: Part(c): Given function is, fx=x33x-4 at 4,2 To find the gradient of a function (which is a vector),…

Q: d'y Find for dr? y = 5x? cos(x) + 13 sin(x) d?y dz? ||

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Q: VE-1 x= sec?t b) Find for y = dx sint

A: y=t-1sintDifferentiate w.r.t 't'dydt=sint·12t-1-t-1…

Q: 4. Find . d?y of the functions x = 1+ cost and y = 1– sin t. dx2

A: Differentiating given parametric equationswith respect to t,x=1+costdxdt=-sint…

Q: Find dy and evaluate when x = T and dx 0.5 for the function y -10 cos (5x)

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Q: 14. Solve the equation d?x dx dt +2x sin 3 dr? dx given that at t= 0, x = 0 and %3D dt ment

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Q: Find the general solution of : x tan?y dx + (1+ Vx) dy = 0

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

Q: Q1) Solve the following ordinary differentiai eyilation: (x + y)dy = dx

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Q: Q3 Find dy/dx on the graph y sec/x+ y? = cos2x at point (1, 2).

A: We have to find dy/dx at (1,2).

Q: If we solve the DE y dx + 2 x dy 0 alter converting it to Exad using an

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Q: B. Substitution as suggested by the equation 3. (x + 2y – 1)dx + 3(x+ 2y)dy = 0 when y(0) 4.…

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Q: Q1: Find dy/dx for the following functions:- (1) e – 3* = x sinh y (2) tan-12 = (Inx' + y²)

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Q: Find by definition for the following : dx 1. y = (2x² + 1) 2. y = cosx 3. y = sin?x

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Q: Solve the following 1 1) y dx + x² + y? dy = 0 x +y 2) (3x? In x+ x² –y) dx- xdy = 0, y(1) = 5 dy…

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Q: Solve by finding an I.F 1. xdy – ydx = (x² + y² }£x y - sin x 2. dy + -dx = 0 ......

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: d'y Using method of variation of parameters solve + 4y = 4 tan 2x dx?

A: d2ydx2+4y=4tan2x

Q: Solve the following by Substitution Method. 1. y(x tanx + In y)dx + tanx dy = 0 dy 2. = (-5x + y)² –…

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Q: 4. Find d?y/dx² for the following functions: a) y = sin x? cos 2x b) y = cos (sec2 3x) c) y = x²(x³…

A: Since you have asked multiple questions, we are answering the first question for you as of now. If…

Q: The µ(x) that converts the equation below into an exact equation x dy (x*ev ++ (2x²e" + 1) = 0 y) dx…

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Q: Q2: Find y(2) if D.E as give dy 2. +3y=sin 2x, y(0) = 6 dx Given

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Q: (b) Solve the following initial vahue problem by separation of variable = 2x at x = 0, y=-2 dx

A: We will solve the problem

Q: Q3. Solve the following DEs. 1. 1 dy _ ! Iny = sinx (In y)² у dx

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Q: 1 dy 3 x*y3 y 4 dx

A: Given that    dy/dx -(3/x)y = x4y1/3  Here we have to solve the given differential equation.

Q: Check for exactness and obtain the general solution. 1. (2xy – tany)dx + (x2 – xsec?y)dy = 0

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Q: Solve the given problem below: (2x + y cos x) dx +sinx dy=0

A: We will solve it by exact differential equations method.

Q: Find the solution of the following: 2. e2x (2cosy dx - sinydy) = 0; y(0) = 0 %3D

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

Q: Find the solution of the following: 2. e2x(2cosy dx- sinydy) = 0; y(0) = 0 %3D

A: The given differential equation is e2x2cosydx-sinydy=0 It can be re-written as…

Q: The function y = 4e3x sin x is a solution of dy Зу + 4е3х dx COS X %3! (A) True (в) False

A: Differentiate y with respect to x

Q: Q8// find the general solution (tan-'x + (cotx)y)dx + (lnsinx)dy = 0

A: The differential equation is given as (tan-1x+(cotx)y)dx+(ln sinx)dy=0 Compare it with Mdx+Ndy=0…

Q: Solve the following using the method of undetermined coefficents: d2y/dx2 − 3dy/dx − 4y = 2 sin x.

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Q: Find the general solution to the following equations: dy 2+ tan y dx

A: The given is the differential equation which can be solved as shown in step 2.

Q: Solve for C using the form f(x,y)=C. Given [2x + ycos(xy)] dx + x cos(xy)dy = 0; f(1)-pi/6. decimal…

A: differential equation

Q: Find the solution of the following IVP. * (ye)dx + (xe* + sin(y))dy = 0, y(0) = π

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Q: Use the method of variation of parameters to determine a particular solution to the given equation.…

A: Solution is given below