f (x) = 4 cos ( %3D

Q: x sin x dx = kr, then the value of k is equal to

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Q: b. f(x)dx

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Q: 2x(y+1)dx-ydy=0

A: We have,2x(y+1)dx-ydy=0 seperate x and y terms2xdx = yy+1dyIntegrate both sides∫2xdx =∫ yy+1dy =…

Q: Solve four questions of the following DEs xy dy + (x^2+y^2) dx=0

A: Given equation is homogeneous differential equation

Q: 3. xe' ty dx = xydy

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Q: 5. (x + 2y - 1) dx - ( 2x + y-5 :) dy = 0

A: Let's find.

Q: 1. Find the general solution of 2 ylnx dx = (x+¹) ²

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Q: Solve the following equation. ln y = 3

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Q: If 8 (x) = | sinx dx and g| |=3, then g (0) is equal to A 2 -2 D 4 B.

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: x(2y – 3)dx + (x2 + 1)dy = 0

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Q: (у2 — 2ху + 6х)dx — (x2 — 2ху + 2)dy 3D 0 - -

A: Compare with exact differential equation then solve

Q: ч.) -17x° - 4 x + 3) ·dx

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Q: 2 3 x 3 8 + x° •dx 6.

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Q: Solve the following D-E 1) y' + y = sinx

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

Q: Evaluate the following and show all necessary solutions. Enclose your final answer. (x² + 1)dx | 5…

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Q: x2 +1 3. xe dy + dx = 0

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Q: cos" (x)dx COS

A: Integrate by substitution

Q: 1. (x + y) dx + (:

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Q: Evaluate: 0 xsinx 1 + x² dx

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Q: +y = e=* sin x

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Q: 3. ( 3x + 2y +7) dx + ( 2x – y )dy = 0

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Q: 5. Solve the equation (D + 1)y = sin x

A: 5 ans

Q: (2x+y-3) dx + (x-4y + 1 ) dy = 0 %3D

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Q: Evaluate V3x? +5 dx

A: Recall: Some integration formulas:  ∫dxx2-a2=12alogx-ax+a+c ∫a2+x2dx=x2a2+x2+a22logx+x2+a2+c  ;…

Q: If  f(x) = ex,  find  f(ln(2)).  (Simplify your answer completely.)

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Q: Part I Solve for the general solution of the following equations: (x* +3y)dx – xdy = 0 а.

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Q: | (1+2x) e#dx

A: If the limit exists and is a finite number, we say the improper integral converges . If the limit is…

Q: 56. dx x In x

A: Given improper integral ∫2∞1xlnxdx   ∫1∞1xpdx  is convergent if p>1  and divergent p≤1

Q: cos x dx 1 - cos? x d)

A: We have to find the antiderivative if the given part d.

Q: Solve (e' +1) cos x dx +e'sinxdy = 0

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Q: 35. x dx + Ja? - x² dy = 0. ,2

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Q: Solve the equation for x .   a)ln(1 + e-x ) = 3       b)sin x = 0.3

A: we have to solve for x in the equations        ln(1+e-x)=31+e-x=e3…

Q: Solve the following D. E y' + y tan x Cos X ニ

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Q: 1. x sin x dx = log y dy %3D

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Q: 1 dx 5х e

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Q: Solve the following by indicating the steps and describe the process: sinx dx SCOS² 1.

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

Q: 1. Find the general solution of dy = e 3x+2y dx

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Q: 7. (x-2) dx + 4( x+ y-1) dy = 0

A: Given : (x - 2)dx + 4(x + y - 1)dy

Q: dx 2. when X=4 y =1

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Q: dy x[2 In (x)+1] %3D dx sin y+y cosy

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Q: Solve the following equation for x. arcsin(x) + 2 arctan(x) = T Enter your answer rounded to three…

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Q: 1. Evaluate roo (a) /(1-2)e* dx

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Q: •1.5 а. х In x dx

A: (a) Given integral is ∫11.5x2lnxdx Here, a=1 and b=1.5 Now, a+b2=1.25 First compute Sa,b, which is…

Q: sinh (2xV1+x? dx

A: Given:         ddxsinh-12x1+x2          Apply differentiation rule:       sinh-1ux'=1ux2+1·u'(x)…

Q: 1+ x² dx (e)

A: Apply trigonometric substitution Let x= tan(theta)

Q: (x-1) dx- ( 3x- 2y- 5 ) dy = 0

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Q: Solve the following differenti- d'y 3. +2y=e"; dx dx

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Q: 6. (2ху + x) dx + (x2 + у) dy 3 0

A: the given differential equation is: 2xy+xdx+x2+ydy=0 we have to solve the given differential…

Q: Find the general solution of nx dx = (x + 1)² ylnx

A: