1 3- S-x2 3 S y, dx 3 4- J2 (x+3)*

Q: Find y(4) = d4 y/dx4 if y = -2 sin x

A: Given y=-2sin(x)

Q: 3. f 3/2 y dydx (I wz dx dy dz. 4.

A:

Q: 3 9 dx dt -1 -3 with x(0) : 4 Give your solution in real form. X1 = X2 = 2. II

A: The objective is to solve the differential equation:

Q: O)³ = /1+ (y')² = /1+ (y')* = 3 + d²y dx2 a3y 3? +1 ax3 at

A: Note:  according to our guidelines we can answer only first three subparts To determine the order…

Q: a. By differentiating x2 - y2 = 1 implicitly, show that dy/dx = x/y. b. Then show that d2y/dx2 =…

A: The given equation is

Q: Find the set of solutions (3x – 3y – 2) dx – (x – y + 1) dy = 0. - - %3D

A: Given differential equation is linear, we will use substitution to solve it

Q: 3x² (- x) dx – (-y) dy = 0 2х (1) Find the general solution for

A: The given differential equation is: 2xy3-xdx-3x2y4-ydy=0 Comparing this with: M dx + N dy = 0, we…

Q: dz and dy dz 3. If x? – 3yz2 + xyz – 2 = 0, find -

A: In this question we have to find the dzdx and dzdy.

Q: dy x³ - 2y² f) 3 Hint: You know two methods that will work! %3D dx 4ху

A:

Q: 2 √2x-x² SJ J² J²^ √√√x² + y² + 2 00 y²)[2x − (x² + y²)]dydx -

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Q: Obtain the particular solution when x = 1 and y = 1 3 y°) dx 3 - x(x + y) dy = 0

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Q: Find the General and Particular solution of = 4y ; y= 3,when x = 0 dx

A: Given: dydx=4y

Q: dy * + 2(t + 1)y² = 0, _y(0) = - ip 1/8

A:

Q: B. Solve the followina equation using the dete 3. 2y(x2 -y + x) dx + (x2- 2y) dy = 0

A: Given,                  2y(x2-y+x)dx+(x2-2y)dy=0

Q: (x+1 0SxS2 f(x) = { Then what is the result of| ($2) dz 5

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Q: 4.2(х — у)dx + (3х — у — 1)dy 3 0

A: Let's find.

Q: (ost) X= 3サ-3 DiD X-2-2y ¥ーにh で3,0) D3 Dy メーと2 サ=スメート X-4 <-リ-3 toノー4)

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Q: Q3. Solve dy (x+3) dx S 3x, 0 3.

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Q: Solve equatian. the differentiql dy = 80-2y * Such that y=70 when x=0

A:

Q: V1-y² -1 0 kpxpzp (,x + zA),I „«-,S

A: The given integral is: I=∫-11∫01-y2∫0x y2+x2 dz dx dy

Q: Q4. Evaluate : O (xy²) dx dy -√1-(x-1)²

A:

Q: V16-x² .4 Evaluate: [4 16-x² J/x²+y² dz dy dx

A: We will evaluate the following Integral.

Q: ii) x*(1-y³)dx+y(1+x³)dy=0

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

Q: dy 15 +4y-042

A: ∫115+4y-4y2dy

Q: 4) x dy-ydx=(x²+xy-2 y²)dx

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

Q: Find the General and Particular solution of = 3y ; y= 3,when x = dx

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Q: 2 dy さx-= e

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Q: Find the particular solution: (y4 – 2xy) dx + 3.x² dy = 0; when x = 2, y = 1 %3D

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Q: q. r. √y² - 25 -dy, y > 5 y³ dx x²√√x²-1 2 ,x > 1

A: Solve both integral as following:-

Q: I Solve the fllowing FODF 2y(x+y+2) dx + (y²-x²_ 4x-1)dy = o when x=2,y= 3

A:

Q: How I show that if Y=ax^2 that (d/dx)=2ax(d/dY)?

A: The given expression is y=ax2.In order to prove the given expression, use the following definition.

Q: 3,3 (xyリdk+ x°dy : 0

A:

Q: (x³ + y² + z) dx dy dz. 2 Evaluate

A: To evaluate the integral

Q: у (4х + у) da 2 (x² – y) dy - - 2x2 + x + 2 ln y = C ans.

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Q: = 2-x² and f'(2) dy when x = 1. dx 8. Let y f(1+ Ju), - 3.Find

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Q: QI Find dy for 2y2/3+xy3/20 x 0

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Q: |(2 f(x)+3) dx=19 f(x)dx then equals?

A: ∫afx+bdx = a∫fxdx+∫bdx

Q: 2.2 (x²-y² + sxy + 2) y.dx + ( x + ² + 4xy + 2)x.dy=0

A:

Q: ๆ ³₁₂₁ (4x²y — z³) dz dy dx -2 J1

A:

Q: Q9// find the general solution (sec³x + (cotx)y)dx + (Insinx)dy = 0

A: Answer and explanation is given below...

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

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Q: Find an implicit general solution of ( x² + dx + 1+ 4x²y², - y*) dy = 0 %3D 1+4x²y?

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Q: V1-x² e-(x²+y²) dy dx

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Q: Q3) Solve (ysin x + y²) dx – („+1 xsoɔ + *) - - 2xy) dy = 0

A: 3 Given differential equation is ysinx+y2dx−1y2+1+cosx−2xydy=0.......1. We have to find the solution…

Q: Evaluate В: А: 3e-422 dz Jye-y dy 0, 0,

A: In the question it is asked to calculate the integral of two functions given below: ∫0∞ye-y3dy…

Q: y" – 10y' + 34y = 3x2 + x – 1 || | (D² – 10D + 34)y = -cos3x

A: 1-D-1 = 1+D+D2+D3+.... Note : As per our Guidelines, we are supposed to answer first question.

Q: 2. Find in terms of Jo and J,: x²½(x)dx

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Q: .3 2х+x-1 4. J dx х3+x2—4х-4

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Q: 1-y Q2: Evaluate fo y²(x² + y²)dx dy -1

A:

Q: | 3yVT – 3y² dy

A: