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

Q: Q2: - If y = 3 sec3t and x = etan3t prove that: - dy (In3)² ,Y logy x %3D dx

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Q: find dy/dx.1. y = -10x + 3 cos x            2. y = 3/x + 5 sin x3. y = x2 cos x…

A: Given the functions :- 1.  y = -10x + 3 cos x Differentiating with respect to x dydx =…

Q: (a) | (2x cos y + sin x) dx 6. */2 (b) I| (2xcosy+ sin x) dx dy

A: Solving integral

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y' = y2/√x and y(1) = -1.  What is the exact…

A: In the given question, it is asked to solve a differential equation using Euler’s method.

Q: . (solve exact de) (2ysinxcosx - y + 2y?e*v* )dx = (x - sin?x - 4xye*)dy

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Q: Solve: sin(y) dy/dx = e

A: given question is solved using variable separable method of differential equation    final answer is…

Q: dx ylnx- dy y + 1₂ X 2

A: given :ylnxdxdy=y+1x2

Q: 7) Find dx 4e* dy if y = %3D 8) Find the first derivative of f (x) = sin? (x°).

A: We need to find out : 7)  dydx if y=4exx 8) First derivative of f(x)=sin2(x3)

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

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Q: Find dz/dx and dz/dy for: x² sin (y³) + xe32 – cos(z²) = 3y – 6z + 8

A: Here, the given equation is: x2sin(y3)+xe3z-cos(z2)=3y-6z+8...(1) So, z is a function of x and y

Q: Find the general solution of dy 2+ sin (x) dx 3(y – 1)² |

A: given,       dydx=2+sinx3y-12

Q: dy Determine the general solution of = 1+ 3y tanx. dx

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Q: Solve ODE for general solution: (2ysin(x)cos(x)-y+2y^(2)e^(xy^2))dx=(x-sin^2(x)-4xye^(xy^2)dy

A: Hence the given ode is exact. Obtain the general solution as follows,

Q: Find the derivative of cos(0)d0. du Jo cos(0)de = cos (w²) · 2w • d de So" cos(8)d0 = cos(2w) • d S…

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Q: Find the general solution for -x) dx - (-y) dy dy = 0

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Q: Find the general solution of 2ydx + (x – sin Jy)dy = 0.

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Q: If y= sin f dt, then dy is dx 2x sin x sin x 2 VX sinx 2x sinx

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Q: b. sin 2xdy – 2(y - cosx)dx = 0; when x = 1/4, y = 0

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Q: Obtain the general solution using separation of variables x cos² y dx + tan y dy= 0

A: Given differential equation is: x cos2y dx+tany dy=0 Apply variable separable: tanycos2ydy=-xdx…

Q: What is the integrating factor of the D.E. 2y dx + (x- sin vy) dy =0 ?

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Q: dy Find the particular solution of 2y- = x+ sin a when y (0) = 1

A: we have to integrate both side , we get

Q: If y = f(x) is the solution of (-x – 9)dx + (x2 + 10x + 41)dy = 0, f(0) = }In(41) +arctan(5/4), then

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Q: find dy/dt. y = sin (cos (2t - 5))

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Q: (solve exact de) (2ysinxcosx - y + 2y²e*v¨ )dx = (x - sin'x - 4xye )dy

A:

Q: Use the Euler method with dx = 0.2 to estimate y(2) if y' = y/x and y(1) = 2.  What is the exact…

A: Given: dx=0.2 y'=yx and y(1)=2

Q: Find the particular solution for the given separable equation when y(0) = 3. 1 dy = ysin(2x) 1? dx

A: To find the particular solution for the given separable equation when y(0)=3

Q: Using dx/dy solve sin(x+y)-cos(x+y)=1

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Q: 8/ (e* sin y +3y)dx -(3x-e* sin y)dy = 0

A: Given thta  The differential equation

Q: Use the Euler method with dx = 0.2 to estimate y(1) if y' = y and y(0) = 1. What is the exact value…

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Q: 1. Solve for y of the Separable D.E. sinx dx +y dy = 0

A: To solve the given differential equation for y.

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

A: Given x2sin2y-5z=1+ycos6zx. To find ∂z∂y.

Q: What is the solution of the equation dey/dx=y/x+tany/x

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Q: 5. y = l 1- co s x 1+co s x

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

Q: Solve the equation xcosy dy+(x+2)siny dx=0.

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Q: 2. f" S"(sinx + cosy) dx dy

A: Note: As per our company guidelines we are supposed to answer the first question only. Kindly ask…

Q: Find the value of dz and dz/ dy at the point A when x changes by (0.01) and y changes by (-0.01) xe…

A: Here we can use the following formula  If z=fx,y, thendz=fx dx+fy dyδzδy=fx δxδy+fy

Q: Whatis the derivative of y = sin (2x − 1)? dx = 2 cos (2x - 1) dy dx = cos 2x dy -2 cos (2x - 1) cos…

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Q: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

A: Given: (3x + 2y3) dx + 3xy2 dy = 0 ,  y(1) = 1

Q: dy 4. Find at (- 2,0), if 3x² +2x²y² +sin y=12+2y. dx

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Solve the Linear DE dy/dx = 1+ 3y tan x

A: I have stated the used formulas in the solution.

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

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

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Q: 9. Find the general solution: (3x²y – sin y)dx + x(x² – cos y)dy = 0

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Q: Find dy/dx implicitly. exy + x2 - y? = 11 |

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Q: ind the particular solution of (dy/dx) = (5x3 + x2 - 2); y = 1 when x = 0

A: The solution of a differential equation with no unknown constants is a particular solution of that…

Q: the initial value DE y' - ytanx = sinx, y(0) = 1 cos 2x 5-cos 2x %3D 4 sin x 5-cos 3x 5-cos 2x В) у…

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Q: Live of y = e(x+ln x) cive of ƒ(x) = 5x6 – sec jye of y = e(sin x) e(sin x) - sin(e

A: We have to find the derivative of the given function

Q: Find the general solution of : x tan²y dx + (1+ Vx ) dy = 0

A: To find the general solution of : x tan2y dx+1+xdy=0

Q: The second derivative d^2y/dx^2 of y^3 = xy + 1 at the point (0,1) is

A: