a. y" -2y' +2y=e*tanx P. y" +y=tanx+e3x-1 . y" +4y=Dtan2x d. 1 -y"+2y=tan 2x- 2

Q: find the integrating factor of cos(x)y'+sin (x)y=2cos^3(x)sin(x)-1

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Q: Find both first partial derivatives. 18y2 x az %3D ax dz ду

A: The given function is:z=18y2x

Q: Show that y = -cosx In(secx + tanx) is a solution of y" +y = tanx

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Q: Suppose that y = 4 cos² t , x = v3 sin(2t) and 0 < t<a. Then dt2

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Q: If y = (2x)sin (4z) , then dy sin(4æ) · (2sin(4z) esin(4z) In(x)) %3D dx X synta

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Q: Find the particular solution for: y' sin(2y) – cosx = 0, x =when y = 0 %3D

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Q: Ssin(2x)dx = cos(2x) + C cos(2x) 2cos(2x) cos(2x) + C O 2 cos(2x)+ C -

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Q: 23 Find dy/dx on the graph y3 sec/x2 + y2 = cos2x at point (1, 2).

A: Use product and chain ruleof differentiation at given value

Q: ind dy/dx of y= tan^-1 (ln x^2

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Q: Find y, of (D² + 1)y = sec x = In |cos x| (cos x) - x sin x В y = x sin x + (cos x) In sec x = x sin…

A: Please see the below picture for detailed solution.

Q: 5- = cos nx dx= [cos nx cos nx dx 0.

A: We have to solve given problem:

Q: 3. Find d²y/dx² of y= x cos (5x) – sin² x/ |

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Q: Differentiate: y = 5 tan? (25z) %3D Oy = -750z tan (25z) sec (25r') Oy = -750z? tan (25z) sec (25z)…

A: We have to differentiate  y = 5 tan225x3.

Q: Evaluate (2x-y)dx+(x+3y)dy along the path C: curve on y = 1-x² from (0,1) to (1,0).

A: Given the line integralI=∫C(2x−y)dx+(x+3y)dyCurve y=1−x2

Q: 3. (16x + 5y)dx + (3x + y)dy = 0 1 (Cos 2y - 3x²y²)dx + (cos 2y - 2x sin 2y - 2x'y)dy 0 the

A: In the given question we have to find the solution of the differential equation 1.…

Q: 4. Integrate COs x dx

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Q: Differentiate : a. y= 9x sec (x/3) b. y= sin2x/1-cos2x

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Q: z = sin(6x) sin(5y) az az dy II

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Q: Find both first partial derivatives. sinh(5x + 4y) az %3D dz %3D ду

A: Explanation of the answer is as follows

Q: Compute dy/dx if sin(x) = cos(xy^2

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Q: That question please

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Q: dy tan tan x = 0 dx coscos x +

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Q: Find partial derivatives of x3sin y + cos2x tan5y with respect to x and y

A: We have to find the partial derivatives of  x3siny+cos2xtan5y with respect to x and y.

Q: Find the general solution of y'= sin²xcosy.

A:

Q: 25. Find x, y, eR from 2coshy - 7sinhx = 3 and coshy - 3 sinh² = 2 %3D

A: The given system of equation: 2cosh(y)-7sinh(x)=3                    ......  (1)cosh(y)-3sinh(x)=2…

Q: 2. [2x*tan y – ysin (2) – 1] dx + [xsin (2) + x*sec*y] dy =

A:

Q: b) Find if Scosy Vt3 + 5 dt + tany = x -sinx b) Find if S* Vt2 + 5 dt + siny = x – x°cosy dx2

A: Solve by differentiation

Q: 2 Express the flowing equation in Cartesian equationr = 1-cos e

A: The given polar equation is: r=21-cosθ

Q: 2. if 2x3 +10 x?siny-y"tanx = 0 ノ the y' so dy write ex pressin in terms of X and y.

A: Applying implicit derivative we have

Q: 2. sin3x dx + 2y cos 3x dy = 0

A: Given equation - sin(3x)dx+2ycos33xdy = 02ycos33xdy =-sin3xdxydy =-sin3x2cos33xdx             Taking…

Q: 1. cos(xy) + secy = 5 2. Arcsin(x/y) = 4x + 3y 3. 4ln(Arctan x) = 1- y 4. y = 5/(sin3x +cos3x) 5.…

A: we have to derivative two times

Q: arctan(*) 1+e2kx dx =? A) arctan(e*)In|cos(arctan(e*)| + S in |cos(arctan(e**)dz]+ c kekx 1+e2kx B)…

A: ∫arctan(ekx)1+e2kxdxFormula to be used :1.Intergration  by parts2.Substitution3.ddxarctan(ekx) =…

Q: 1- S7 cos(y)eSin(y)+9X dydx

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Q: obtain in alinear differential eqaution with real, constant coefficients that is satisfied by the…

A: The solution of the problem is given in the next step.

Q: Solve the initial value DE y' - ytanx = sinx, y(0) = 1 5-cos 2x 5-cos 3x 5-c A) y B) y = с) у %3D 4…

A: Given differential equation is y'-ytanx=sinx,   y0=1 Compare the given differential equation with…

Q: = Solve: Cony siny dx + dy. cosr sinx

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Q: u = xz siny + yz cosx + xy tanz

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Q: 2- Find of y = dy dx y %3D /cos-1(In (xy))

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Q: Find dy/dx of x siny + y = 4x + 3

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Q: cos²x sinx dy + (y cos³x − 2)dx = 0

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Q: Classify the partial differential equation +34 = sin(3x + 4y).

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Q: Find all the second partial derivative T = e-4r cos(0) -4r, Trr 16e 'cos (0) %3D Tre = 4e -4r,…

A: “Since you have posted a question with multiple sub-parts, we will solve the first three subparts…

Q: 1) (2cos³xsin x – ysin x – 1)dx – cos x dy = 0 ; when y ) = 3v2

A:

Q: d'y dy dx² dx 21 29 - -6y=6e¹ cos x; when x=0, 20 dy dx =-629 y = 2e-3x - 2e²x 3e-* 29 (3 sin x - 7…

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Q: 1) S 2 sec y (tany – sec y) dy

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

Q: Find (dy/dx) for: tan-¹(x + y) + In(x³y) = sinh(y)

A: To find dydx for: tan-1x+y+lnx3y=πsinhy

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: