d²x y? + 1 a. y ay? %3D dy2 by()° (dx d²x x² +1 dy. dy2 d³s С. dy3 d²s dx² (ap)' 2 (dv)² + 2.

Q: 8-x²-y? 19. 'dz dx dy +y²

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Q: dy 3. + + 2y + y² = 0,yı = -2 dx

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Q: 8. dy dx || = -X y

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Q: 5 (x² + y² )dx dy -5 J –1

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Q: H2. 2dy dy dr2 d²y dy :1 at x = 0. dx – 52+2y= 2x², y=7 and - dx

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Q: (») LLa (1-y? In(x² + y² + 1) dx dy 1-у2

A: Given: ∫-11∫-1-y21-y2    lnx2+y2+1dxdy

Q: 8. y dx = (3x + y³ – y²) dy; when x=1, y=-1

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Q: dy ху+3x-у-3 7. Ans: y-x+In y+3, %3D = C dx ху-2х+4у-8

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Q: d?y dy 2- 8y = 8x? + 20x + 2, at y(0) = 0 and y(0) = -8 dx? dx

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Q: dy 3 1 +-y = 27y3 Inx, x > 0 dx

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Q: y(2x? - xy + 1) dx + (x - y) dy = 0, ANS. y(2x – y) = c exp (-x?).

A: Given differential equation is y(2x2-xy+1)dx+(x-y)dy=0

Q: dy + 4 y = x³ - dx

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Q: 2x dy 2х. -y = x² - x; y(4) =2 dx

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Q: Evaluate the integrals

A: The given integral is ∫02∫03y∫x2+3y28-x2-y2dzdxdy.

Q: d²y ex 1. Find dx2 for y = %3D (2x²–3)

A: According to our terms and conditions I have solved first question for next question repost

Q: 16- y? V16 - x2 x dx dy 2.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Obtain the particular solution when x = 1 and y = 1 yl? - y² + 1) dn - xlx? - y? - 1) dy = dx – x(x²…

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Q: = 6 + 3t, y = −8t;  dy dx

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Q: dy y? – 1 y(2) = 2 %3D dx x2 – 1' -

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Q: Solve the differential equation in Exercises

A: Given 17. dydx=2x1-y2 ,   -1<y<1 18. dydx=e2x-yex+y

Q: (y* - 2xy)dx + 3x?dy = 0; when x = 2, y = 1

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Q: dy dy dx +3. + 2y = 0, subject to y(0) = 2 and y'(0) = –6 dx2

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Q: (3-y)dx + (y-2=) dy = 0, y(-1) = 2. ry2

A: Given: 3-yx2dx+y-2xxy2dy=0, y(-1)=2

Q: 2. (2-x) dx + 2r y dy = 0 Ans.

A: As per our guidelines, we are supposed to solve only one question.Please repost the remainning…

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

A: Solve both integral as following:-

Q: dy 1.3- |4 - х2 ys dx : у(1) %3D 1

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Q: C. dy b. 4 sin 2x> , y = 2, when x = 2 %3D dx dy С. dx = x + 3+ e2x>, y = -1, when x =

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Q: y(4x+y)dx-2(x2-y)dy = 0  when x = 1 , y= 1

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Q: 5/xy dy -2, х, у» 0 dx y =

A: See the details solution in below

Q: dy Find dx2 4 if y = x cos(x) d²y dx? ||

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Q: 23. dx + 4y = 0; y = cje2 + czxe2x dx d'y + 2x - x + y = 12x²; dy 24. x dx dx "dx y = cx- + czx +…

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Q: dy -y- dx 2x, given that when y=0, x=+2

A: We need to solve the given differential equation with its initial conditions. As the equation is of…

Q: 24. dy + y = 12r; dx r + 2r dx dx

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Q: 1 Given y = 3x5 + -, dy is equal to 2x3 dx

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Q: Find 2," dy d²y dx ' dx? d3y and from: dx3 3. x = 1 – t? and y = 2t3 – t2 + 1

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Q: 32. (2x-y+4) dx + (x-2y-2) dy = 0

A: Consider the differential equation(2x-y+4) dx+(x-2y-2) dy=0. The objective is to solve the…

Q: d²x = y² + 1 а. y dy2 y (* + - ** + 1 dx, 2 d²x x² + 1 dy² d's d²s С. dy3 dx? () = x² + 1 dp. d. y…

A: An ordinary differential equation is an equation involving only one independent variable

Q: dy 2 = 3, ,3 X'y' - xy dx

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Q: %3D 4x3 dx 2. х3dy + 3x?y dx 3. х3 dy + (3x?у — хе*) dx %3D 0 -

A: These are the first order and first degree DE. Solutions are given below:

Q: Solve for dy when y = + 3x, x=2 and dx =0.5

A: The given problem is related to total differentiation.

Q: r1-x 2–2z 31. dy dz dx

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Q: 2x - y + 5) dx - (2x + y) dy = 0 where x= 3, y=7

A: Let's find.

Q: d?y 7. y = e2" – 3e-, dx? dy - 2y = 0 dx

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Q: (x - y) dx + (3x + y) dy = 0; when x = 2, y = -1.

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Q: dy = a-x dx when x 1, y = 2 when x = 2, y = 0 %3D what is the value of a?

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Q: dy -(3tan x)y = 1 dx 2.

A: Given that, The differential equation is following, dydx - (3tanx)y = 1 We have to solve the DE.

Q: d²y dy dy %3D 1 2. dx2 6y = 0, when x - 0, y = 2, - %3D dx dx

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Q: dy 2 ,? cosx +-y = -x²y dx %3D

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