1?y" + 4ty' - 4y = 0; y(1) = 5, y'(1) = %3D %3D

Q: y(ln x – In y) dx = (x ln x – x In y – y) dy %3D - -

A: This is the question of differential equations.

Q: integral (In x) 3  dx

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Q: Reducible to Exact (2xy ln y)dx+(x2+y2√y2+1)dy=0 Have to be convert to exact by integration method

A: Given  Differntial equation (2xy ln y)dx+(x2+y2√y2+1)dy=0

Q: `s): The area of the surface obtained by rotating the curve y = ln(3x - 2), for 3 ≤ x ≤ e², about…

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Q: (1) Find the general solution for -) dx - -) dy = %3D

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Q: 1. Integrating factors found by inspection: (xy + xy)dx+(x²y²-2)dy = 0

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Q: Evaluate the double integral : (y³ – 12x) dx dy -

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Q: (10) Find x²e*y dx dy. (Hint: Reverse order of integration.)

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Q: Find the general solution Using Integrating Factors Found by Inspection. Show complete solution.…

A: Find the general solution Using Integrating Factors Found by Inspection. Show complete solution.…

Q: find derivatines of the first derivatives indol and Zuotients.. y= tanx %3D

A: Given function is y=extan−1x Use formula ddxex=ex and ddxtan−1x=11+x2 Differentiate y=extan−1x with…

Q: Show that the equalion Compatible 3olutions are and also find its रिकेपन nd देक.र

A: P2+q2 =1 given therefore 1x =pz P =x/z.  ...(1) q2 =1-p2      =(z2 -x2)/z2 q =z2-x2z ....(2)

Q: 6) dx X 3 Type 2 mproper integral 1-

A: We use Type II improper integral  Here at x=0 f(x) is discontinuous so we break the limit at x=0 If…

Q: 8. cos xsin y dx +(3xy+sin x cos y) dy C:boundary of the region lying between the graphs of y= and y…

A: Given:  ∫Ccosxsinydx+(3xy+sinxcosy)dy...................(i) where C is bounded by y=x4  and  y=x To…

Q: x2 dy dx by reversing the order of integration. 4/x 1. Evaluate

A: Given double integral is∫14 ∫4x4x2 dy dxNow , By interchanging the integral we have ,∫y=14…

Q: In x 2. Integrate -dx , (i) using the sub stitution u = Inx (ii) using integration by parts.

A: Integrate by substitutions and by parts

Q: 6.) y'of y = Insin(arctan 3x)

A: This is a basic differentiation question

Q: 2. Evaluade integral.. iterated double ze^ dx dy

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Q: Sz x² sin 2x dx (Integration by Parts)

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Q: Q3) Reversing the order of integration 2 y² sinxy dy dx

A: Explanation of the solution is given below...

Q: Integral from 1 to e of 5t^2 lnt dt

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Q: 10 Describe a first step in integrating /2 dx. - 4x + 5

A: Given: ∫10x2-4x+5dx Step 1: Taking the constant term outside

Q: 1. S ( cos(2x-1) dx (Integration by Parts) et

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Q: 6° Szx dx t yay where L cs parabol y=-x(x-) arc

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Q: 2 Evaluate the inteyral. dx dy dz taken. throughout the volumeofsphere 23=

A: We have to solve given integral:

Q: differentiatin, detamina dy of ; dx y= [at) (Xts) (a-z) (x-+)

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Q: 8. dx +x2 Integrate:

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Q: 2. se integration by pacts to eval integralig x² In (3x)dx niz

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Q: A cylindrical shell has a thickness of 0.2 cm. Using differentials, approximate the volume of the…

A: Solution.

Q: integral from -1 to 1 of arccos (y) dy

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Q: find the total differential dz. xety

A: dz=∂z∂xdx+∂z∂ydy ---->1Consider z=xex+ythen∂z∂x=ex+y+xex+y∂z∂y=xex+y

Q: 2sin(y)cos(y) sint(y)+costy) dy

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Q: Estimate the value of integral 3 to 1 dx/x

A: Given,  ∫131xdx

Q: 4. S 2z3 el-z dz 5. S Vx In(Vx) dx Vr3 6. Si, Inx dx

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Q: 6) S sech? (2x- 3) dx | ex-e-x 7) S ex+e-x 8) S(eax – e-ax) dx sinh x 9) S dx 1+cosh x 10) ſ csch? x…

A: Given

Q: 2Linear edluotion 5. dy dx

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: y=ln(θ+4) dy/dθ=

A: Given function :

Q: 8) S(eax - e-ax) dx 9) S; sinh x dx 1+cosh x

A: Answer to question number 8 and 9 are as below,

Q: 3/ Find Value of integral ) dx 0 X+1

A: I am attaching image so that you understand each and every step.

Q: 6. Carefully interchange the order of integration to evaluate os(x/²) dx dy. COS -1

A: To evaluate: ∫-11∫y21cos(x3/2)dxdy by changing order of integration.

Q: Integral of | 4sinxcos cos |dx 1. J sin 9x cos4x dx J cos 2x cos (-x)dx 2. 3.

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Q: Change the order of in tegration 10 10 dy dx

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Q: Sulve the dffeanlial equalion ly). clox Ylx)=16

A: Given:     dydx+y=16

Q: integral In x 2 dx

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Q: What is the (a). general solution to xydx-(x+2) dy=0? (b) integrate.

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Q: * Find the intergration: dy

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Q: {dy}/{dx} for y=4sin^{-1}(x^2)

A: The explanation of answer as follows

Q: x e* dx

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Q: 34. e4x cos 2x dx

A: Solution:Given∫ e4x cos 2x dxFormula:∫udv=uv-∫vdu∫sin ax dx=-cos axa+C∫cos ax dx=-sin axa+C∫eax…

Q: 2. Find the linear approximation to y = sinh (3x) at x=2. State your answer in both exact form and…

A: Find the linear approximation of f(x) at a point x=2

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.