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## Related Calculus Q&A

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Q: tan-1 (xy)=3x2+sin-1(y) find dy/dt

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Q: (y-cos^2 x) dx + cos x dy = 0

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Q: 1 (sin-ix + y) dx + sec-1xdy = 0 xVx² – 1 إجابة

A: The detailed solution is as follows below:

Q: xy" - y' + 4x y= 0, x> 0; y,(x) = = sin x

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Q: y(cos 2x)e*y – 2(sin 2x)e*y + 2x + [x(cos 2x)e*y – 3] = 0 %3D dx

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Q: '+y- y²(cos 2x– sin 2x) = 0

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Q: ау 47. = cos 2x, y(0) = 3 dx

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Q: Find the area of the given region.

A: Consider the function: y=sin 3x·cos 2x. Find the area enclosed by the curve and x-axis in the…

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Q: 2y sin x cos x - y + 2y²e*y") dx = (x – sin²x – 4xye**) dy -

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Q: y'of y = e-2*sin 3x

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Q: iii- y +y tan .* sin 2x, y(0) = 1. (Bernoulli Equation) %3D

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Q: 3. sin x cos y dx + cos x sin y dy

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Q: 3) y sin-ly² dy

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Q: 3) y sin-ly² dy

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Q: X*-y sin cx) = xー Y Sin Cx) =

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Q: 1 (sin-ix + y)dx + sec-xdy = 0 xvx² – 1

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Q: 1. sin'y (2-3 cos y )dy

A: Given: ∫sin3y(2-3cosy)2dy

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Q: cos x – sin x)dx + (2y sin x + 2)dy = 0 (Exact) %3D -

A: To find the solution of the exact differential equation

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Q: (sin y- y sin x)dx + (cosx + x cos y)dy = 0

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

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Q: dy Y - sin sin-* = 0 ソーx || dx 3.

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Q: x+y 2cos sin 2 х-у

A: We know, the difference formula of sine is given by: sinC-sinD=2cos(C+D2)sin(C-D2) Hence,…

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Q: y sin-1y2 dy

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Q: (3x² – 2xy+ y²) dx + (2xy – x² + sin y) dy = 0, y(12) = 0 - |

A: We have to find the required solution of…

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Q: tan-1 y y² +1 tan-1 y ) dy

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

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Q: 1I) (3y cos(3x)dx-sin(3x)dy)/ y 0

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

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

A: Given thta The differential equation

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Q: (- + 2 cos 2x ) dx + (- - 2 sin 2y ) dy = x2

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Q: (cos 2y - 3x²d²)dx + (cos 2y − 2x sin 2y − 2x³y) dy = 0

A: The differential equation is given as cos 2y - 3x2y2dx+cos 2y - 2xsin 2y-2x3ydy = 0 Compare it with…

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

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Q: Solve sin dy -1 = x + y \dx)

A: Differential equation

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Q: 11/ (cos y+ y cos x)dx + (sin x – xsin y)dy =

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Q: 3. sin y(x+sin y)dx + 2x² cos ydy = 0 0: uhen v-2

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Q: 3 - y cos xy - 4x ) dx + (- 2x+3y x cos xy + 2y) dy = 0 - | 2x+3y 2.

A: Compare the given equation with Mdx+Ndy=0 to obtain M and N. Calculate the partial derivatives of M…

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Q: y (0, 3) y = 1 - sin (x - T/2)

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Q: (sin-*x+ 1 y)dx + sec-xdy = 0 xVx² – 1

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Q: 7. (y + y cos x - ye*) dx + (3x + 3 sin x – 3e*) dy = 0; y (0) = – 1

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Q: sin y(x + sin y)dx + 2x cos ydy = 0

A: Given: sinyx+sinydx+2x2cosy dy=0Bernoulli's equation:dydx+pxy=qxynLet v=y1-nLinear differential…

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Q: sin 3X Sinsy dx = - cos3X ussydy; y@=

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Q: 5x cos dx 2 x3 cos 9x dx X' COS

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Q: y = sin x, y = x, 0 <x < T/4

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Q: 1 + cos x – 2xy): fip y(y + sin x), y(0) = 1. COS I 1+ y? dx

A: To solve the given exact differential equation.

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Q: show that the differential forms in the integrals are exact. Then evaluate the integrals.

A: Given: ∫(1,0,0)(0,1,1)sinycosxdx + cosysinxdy+dz To Show: (a). Differential forms in the integral…

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Q: 5.) y''of y = x(sin Inx – cos Inx)

A: We are given: y=xsinln x- cosln x We need to find y'''

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Q: 33. sin x dx dy х 0,

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Q: Evaluate the iterated integral by converting to polar coordinates.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

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Q: Find the differential of the function y = θ3 sin(6θ)

A: Solution :-

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Q: h(x) = cos*x sin x, [0, ]

A: The function is h(x) = cos4x sinx, on the interval [0, pi]. We have to find the average value of…

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Q: i y = tan-1(x)+ tan-1() dy + 10 dx

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