Show that (In x)² dx = e – 2 Find ſ dx x2+ 5x+6 4х Find f dx (x2 – 4)(x-3)

Q: Vx 3 1- evNīdy dx - 3 y3 e*y dx dy

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Q: 16 (1.) 2XInX 2 dy/dx (2. if 4 = cosh 2 JX +1 %3D 213 dx (3.) 4+x2

A: Question 1 is solved by substitution method. Solving other questions are against the policy of…

Q: What is the general solution of xy(xy5-1)dx + x²(1+xy5)dy=0 ?

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Q: Find the general solution to dy/dx= 6-x^2/2y^3

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Q: (3 - x) dx is equal to ° S (3 − x) dx + ["' (3 + x) dx °₁ (3 - x) dx ° L₁ (3+2)dz + f (3-2) x) dx x)…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find the general solution of dy/dx=x-4/x^2-5x+6

A: Explanation of the answer is as follows

Q: Find the general solution of

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Q: dy If y = (5x + 1)(2x +In x), then will be %3D dx (5x + 1) +) + 5(2x+ In x) A. -1 B. (5x+ 1) - 2. +…

A: The given problem is to find the derivative of given function y=(5x+1)(2x-1+ln(x)) , we can use…

Q: Find the general solution of dy/dx= xy-y/x^2-5x+

A: To find the general solution of the below differential equation. dydx=xy−yx2−5x+6

Q: 7. Solve for dy/dx if x = 2 + t and y = 1 + t2

A: From the given problem: x=2+t;y=1+t2 As we know that the Power law: ddxxn=nxn-1 We know that:…

Q: If x2y3 = 4/27 and dy/dt = 1/2, then what is dx/dt when x = 2?

A: Given:

Q: Example 3: Estimate S, x² dx with n=4 by Midpoint Method. Solution:

A: Here first we will divide the integral range into 4 equal parts and then we will calculate the…

Q: Transforming A S B © D dx secx + 1 7 dz 1-2² 1==323d² -dz 1+z² [1+2²21 2-272 1+z² -dz -dz using…

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Q: solve the differential eq + 2x) dx = = (2y \1+x²y² |dy 1+x²y²

A: The given differential equation is: y1+x2y2+2xdx=2y-x1+x2y2dy

Q: Solve th D.E using Exact -(3x² – 6.xy)dx +(-3xr' – 2y)dy = 0

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Q: Solve the particular solution of 3y(x^2 - 1)dx +(x^3 + 8y - 3x)dy = 0; when x = 0, y = 1

A: The given differential equation is 3yx2-1dx+x3+8y-3xdy=0. The initial condition is x=0 when y=1. The…

Q: (A) Evaluate / (4x – 5) (4/x + 4x) dx. x² + 3x - 6 (B) Find dy -, if y = 3 -)4 when x = 1 %3D dx

A: *we have to perform integration operation in A & differentiation operation in B.

Q: find dy/dx 3x² +5y'x² +4/y, a) x² +4x,/y-5y² = 3 (ans.: 2x 10x'y- Jy

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Q: d’y - 2 y = 5x' + In(x²). dx

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Q: 1. Find dy dx S(x)= e**/2x-5 (6-5x)* (iii) f(x) =

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Q: Determine dy/dx y = (In 2x) - (ln(3x + 1)) 1 3x²+x 3x 1 None of the choices 1 3x²-x

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Q: Find dy dx' i) f(x) = Cos2x Sin²x %3D ii) f(x) = log,(x' +4)* e-* /2x - 5 -3x iii) f(x): (6-5x)'

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

A: Given: dydx=5x3+x2-2; y=1 when x=0

Q: Q4 Find dy for all of : dx 3 x(x-2) 1- y = xvlnx 2- у %3 V x2+1

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Q: sin(2t + ) dt e21-3 4 7 4 4 64e 7

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Q: In x -dx C. d. 5% dx хе fx(2x +1)* dx е. f. In(x + 1)dx x2 dx Vx + 2 g. x4 h. dx Vx5 + 1 4 i. j. 1…

A: From the given problem:   c).   I=∫lnxxdx..1     Let,   lnx=uddxlnx=dudx1x=dudxdx=du Substitute…

Q: find the general solution of dy/dx + (3/x)y=2/x^2 as a function of x

A: Given,           dydx+3xy=2x2

Q: So(VE + vZ)° dx = f° xdx - (Vã + vZ)dx • f;(Vã + v2)dx 6. So x(x² + 1)dx = - S x*dx + f, xdx 7. S'…

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

Q: -32e* – 140 -dx J e2x +9e* + 20

A: We’ll answer the 1st question since we answer only one question at a time. Please submit a new…

Q: -7x f(x, y) = e" sin(4x + 5y) af e^(-7x)(4cos(4x+5y))-7sin(4x+5y) af 5e^(-7x)cos(4x+5y) dy ||

A: Partially differentiate with respect to x and y by using product rule.

Q: 15) 4S(5x)] = x² , then f'(x) = ? %3D dx

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Q: d Show that In dx 1 (a) x+2 x* +3x +2 1 (b) Hence find the exact value of dx in simplest form. r*…

A: iii.a. Quotient rule of differentiation states that ddxfg=f'g-g'fg2 Chain rule of differentiation…

Q: dx -x = ev/2 x3 dy 2)

A: By using linear differetial equation method

Q: (3– 3cos5x)} (3x² +2x-7)² (e - sinx +3x) y= Find dy/dx if

A: That's computational, take a careful look.

Q: Find the general solution of dy (y2 + 4) In x In(y2 + 4)"* %3D dx

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Q: By differentiating x² – y² = 1 implicitly, show that d²y | dx² ||

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Q: (1) f dx x3-2x² (2) S dx x²√ √9-x² (3) fx² sin x dx

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Q: 1,- X73X+2 dx (x+リ) Izafhinx dx Ax. Iォfュース alx dx X43X+2 X+1

A: Since, you have posted multiple, we will solve only first part. If you want solution of other…

Q: dx 1. S. 2x-x2 if y = x° (In x)? . dx 3. S x³e-* dx . 2.

A: Note : as per our guidelines we are supposed to answer only one question if there are multiple…

Q: 1. Solve (6re",x0 b. [3cos 2xsin 7.xdx

A: here we have to evaluate  a) ∫-11w(x)dx if w(x)=6x2ex3,x≤035x-3 , x>0b) ∫3cos2x sin7x dx

Q: Obtain the general solution of x^2 d2y/dx2 -2xdy/dx+2y=sin(lnx)

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Q: 2 - S tần² (3x)sec²(3x)dx

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Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

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Q: 3x 6 1 -In xy dx e-In √x dx +dy +=dx = e-mxx y X

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Q: 2. (x + 1)dy – ydx = 0 3. (3x2y – x2)dx + dy = 0 -

A: 2-Given- x+1dy-ydx=0 To Find- The integrating factor by inspection and solve the differential…

Q: dx 4√/3x-x² 5³-

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Q: Show that d/dx(ln kx) = d/dx(ln x), where x > 0 and k is a positivereal number

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Q: d) Obtain the particular solution of (2x– 3y+4)dx +3(x-1)dy =0; when x=-1, y = 2

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Q: dy 3) xIn x- +y = 2 In x dx

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