dy tanx for y = dx 1-secx 1) dy (1-secx)sec x+secxtan2x dx (1-secx) 2) dy (1-s8cx)secx-secxtan²x I3I

Q: dy tanx (4) Find if y = (sec x)" dx %3D

A: Here, we have the given function in the form of a variable raised to the power variable. Therefore,…

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

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Q: (2y cosx + sin“ x)dx = sin x dy ,when x =",y = 1 5y= 1 %3D X 2

A: 2ycosx+sin4xdx=sinxdy,   x=π2,   y=1:A first order linear ODE has the form of y'x+pxy=qxLet y be the…

Q: 9 dx dy +ytanhx= 2 sinh x dy - 2y = x' cos x 10 x dx

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Q: 2 max f (2х + и)dte dx - 5 — и?, x (0) 3D1,x(2) freet dt

A: Given: maxf=∫02(2x+u)dt dxdt=5-u2,     x(0)=1,      x(2).free

Q: tan20 sec2ede In 2 edx 3. 1. (a² + a²tan²0)² 2ex- 1 x'dx dx x- 1 2. 4. (1+ x2)3

A: As per our policy, only the first three subdivisions will be solved. For the remaining subdivision,…

Q: - sinx) dx 2. 1. (COSX (ax' +b)*x dx 2. 2/3

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Q: (2y cos y - x secy-x tan y)dy = (1 + sin y) dx

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Q: dy sin(2x) Find for y || dx /3 – x2 dy dx II

A: Doing the proboem by obtaining the derivative.

Q: find dy / dx if y2 - x2 - sin xy = 0.

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Q: Find general soulution (x+1)dy/dx +(x+2)y=6xe^-x

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Q: Find dy/dx by implicit differentiation. 8.r2y+ 5yr = -9 y 5y + 16x 2x 4x + 5y dy/dx = %3D

A: Recall: d(u.v)dx=udvdx+ dudxv d(xn)dx=n xn-1 d(c)dx=0 ; where 'c' is any constant.

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

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Q: cosxdx 17. - secx+ tan x [2sin(3x)cos(5x)dx 18. [(sin y +2cos y)'dy 19. 20. ſcot'(2x)dx 21. (sin“…

A: solution is given below

Q: Approximate - -1x+3 -dx using trapezoidal rule with n=4 and Simpson's rule with n=4.

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Q: dy tanx Find dx for y = 1-secz %3D O 1 1) dy (1+secx)secx-secxtan'x dx %3D (1-secx) 2) dy…

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Q: 3. f(x,y) tanx - sec²x - cosy

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Q: dx of xcosy+ycosx=xy

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Q: y = cos“ x, Find dy/dx O dy = - sin(x*) O dy = 4 cos3 x sin x dx O dy = - 4 cos x sin x dx O dy = -…

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Q: dy Find ax for y = sinx tanx %3D dy 1) dx = coSx sinx - sinx târdx sinx tanx O2) dy dx = CoSx tanx -…

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

Q: (2siny + 1)dy : 4 and y(0) = 5. dx What is x when y = x?

A: Given:  2siny+1dydx=4, y0=π2 Using Variable separable  2siny+1dy=4dx Integrating both sides, we get…

Q: find the dy/dx by implicit differentiation. 4. 5x-x^2y^3=2y 5. y^2+2xy^2-3x+1=0 6. xy+2y=x^2

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Q: Find dy/dx of y = sin(x)tan(x)

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Q: Find dy/dx 1. y = x^2(sin^−1 x)^3 2. y = e^tanh x/x^2 − sechx 3. y = tan^−1 (sechx) + sech(tan^−1…

A: We expert are following guidelines.We are supposed to do first question. We have to find dy/dx

Q: dy/dx of y=sec^-1 (5x)

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Q: (2y cosx + sin* x)dx sin x dy, when x = y = =,y= 1

A: Given - 2ycosx + sin3xdx = sinx dy , when x = π2, y = 1 To find - Solve the following differential…

Q: 8. Find dy/dx- y = sin (1 + x^2/1-x^2)

A: I have stated the used formulas in the solution

Q: Find dy/dx y=(7x-1)tan(2x^2-x+9)

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Q: (3 sin y – 5x)dx + 2x2 cot y dy = 0 -

A: Solution :-

Q: 5 dy of: y = |x sin 2 + tan (x") dx 4

A: Given function is y=xsin2x+tan4x75 We have to find dydx. Here, we have to use some rule of…

Q: Use implicit differentiation to find dy/dx and d²y/dx2. x2 +y 2 = 5, at the point (2, 1) dy d2y - 2;…

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Q: Ans: y-x+ In y+3, dy = 7. ху+3x-у-3 dx ху-2x+4y-8

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (8, -3)

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Q: y= sinh-lx then prove that Vx2+1 dx

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Q: 3. f sin³y(2-3cosy)² dy

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Q: 1-f²₁ ¹/²(y² sinx dx dy) 2-√²-dxx2 0 3- f(cscx cotx)² 2 4- f₁² x (x − 3)dx for 5-S²₂ (x³ + √x) dx

A: 1.

Q: tion to (1+ x²) dy + 2xy = 4 that satisfies the initial condition y(0) = 0. dx %3D %3D

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Q: (sinx+1) (cosx+1) dy evaluate dx -If: y =

A: Use the concept for derivative of the form  y = f(x)/g(x)

Q: dy Use an appropriate technique to find dx from x² + y² = (2x² + 2y² -x)*.

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Q: Find dy/dx y = -sec u, u = x- COS X |

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Q: 3. (2х - у - 4) dx - (х-3)dy -0 when x %3 1, y 3D 4.

A: We try to identify and group terms and integrate.

Q: dy Find dx by implicit differentiation. 3 +y = 25 -1 dy 9x а. dx 4y dy b. dx 4x Зу -1 dy 4х с. dx 1…

A: We need to find dydx of x23+y32=25. So,                 x23+y32=25Differentiating both sides wrt…

Q: Test for homogeneity

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Q: Cosx 2) ). y dx+ týž - Sinx (²) dy = уч

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Q: Differentiate implicitly to find dy/dx. cos(x) + tan(xy) + 4 = 3

A: Given: cosx+tanxy+4=3We need to find dydx.Recall the formulas: ddxcosx=-sinx…

Q: Find

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Q: dy Find ax for y = sinx tanx dy O 1) = cosx tanx + sinx sec2x O 2) dy dx = COSX sinx - sinx tanx %3D…

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Q: Evaluate (2x - y) dx + (x + 3y) dy. C: x-axis from (0, 0) to (0, -3) and (0, -3) to (4, -3)

A: To solve the given line integral.