SG3" + y2n + y")(2y2" + 3 y" + 6) dy. ,311

Q: (D² +D- 1)² y = 0 , when x = y = 0 , y' = y" = 1, y" = -1 %3D

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Q: Order One  DE (2x+3)y'=y+(1x+3)1/2; when x=-1, y=0

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Q: What is XY? Y 45° 45° Z.

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Q: 15. (2D2 – D+ 2)y = 0

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Q: 8. y" – y = 5sin²(x); when y(0) = 2, y'(0) = -4 %D

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Q: y? – 12r + 8y = -40 16x2 + 72x-112y = -221 |3D O Option 1 O Option 2 (y+) = -5 (x - }) %3D

A: The given curve is a parabola with vertex at(2,-4) and focus is at (5,-4).

Q: Find 4rye®y? dA, where R [0, 1] × [0, 2]. R

A: The objective is to find the double integration where  R=[0,1]×[0,2]

Q: Tgir.y) = (2ry, 1+2+) and g(1.0)=8, then g(4.1)-9(2.1) =

A: Topic:- calculus

Q: 11. (D² – 2D + 5)y = 0 12. (D² + 9)y = 0

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Q: 3.2 find fxxy: flxiy) Bx*t 2€y?+ qxy!

A: when differentiate with x then y should be constant and when differentiate with y then x should be…

Q: S (a? - y)"y dy

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Q: (D^3 + 2D^2 + 12D - 40)y=0 when x=0, y=0, y'=1, y''=0

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Q: - ***** Giveu : mel- 5x+6y Frud: x aud y i 23 = 6x-44

A:

Q: O A y = -s – 1)? y = -412 + 1 y=D -쇼z2 + 1 O D. y Oc. |

A: Here we have to find the equation of parabola.

Q: Find x²dA where R R = } {(x, y) | 4x² + 16y? < 64

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Q: /| r? dr dy ; N: 1 + y < 4r, I< 2, y 2 0

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Q: (i + 1)?y" – 4(t + 1)y' + 6y = 0. y,(1) = (t + 1)?

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Q: D² + D – 1)²y = 0 ,when x= y= 0 , y' = y''' = 1 , y" = -1

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Q: b) у%3D3—х? and y %3D —1.

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Q: uso a.) y – y = ty², y(0) = 1

A: We have to find the solution of differential equation.

Q: Find the arc legnth over:

A: To determine the arc length of the function.

Q: Vr' +y? ydzdydx x² + y? +z? x²+y² 3 Jo Jo

A: Given:           ∫35∫0x∫0x2+y2ydzdydxx2+y2+z2       ∫0x2+y2yx2+y2+z2dz        =y∫0y2+x21y2+x2+z2dz…

Q: y ce + 3r O y'+6y 2t (t+ 1) O y'+2y = / (1+ 6) 3. y'-2y 61 (t- 1) O y'+ 2y = 61 (1 + 1)

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Q: 2 0. ху dх dy -Vi-(у-1)?

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Q: r+ 2y = 4 3r + 8y %3D I =?

A: Simultaneous equations are two or more equations which involves two or more quantities that are…

Q: ít was 6 (bi-ha)=LL(h,0ha)= HAan 1 (h)=

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Q: dy 3. 9+y? メーNE _ xp

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Q: OA. y-1=-2(x- 3) B. y-1=-2(x+ 3) C. y+1=-2(x-3) OD. y+1=-2(x+3) Revie

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Q: 2eх - у- е %3D 0

A: Given: The equation of the curve is f(x) = x ex and x = 1 .

Q: + y² = 0.1, then ces)

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Q: i. BC if x = 2 and y =2

A: In right angle triangle BOC.

Q: 7. у %3DV1+ vx 8. Зx?у — 8х + 4у %3D х3 — 5у?

A: 7) dydx=121+x12x=14x1+x

Q: 7. y' = - 2ry %3D %3D ds

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Q: Q7// Evaluate y y2-64 dy

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Q: 1 d. y = Vx6+1 Rewrite y = y'3=

A: (d).   The given function is: y=1x6+1

Q: What is the value of +3x-2z if x = 3, y=5, and z=4?| 3y 82 OC 18 OD 32

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Q: 3 dy 4y-3

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Q: 3y(y+7) Simplify (y+7)(v² – 9), under what conditions is this expression undefined?

A: Given a fraction : 3y(y+7)(y+7)(y2-9) We have to simplify it and also determine under what…

Q: R Q QS = (-12+x) yd; OS = yd 6. %3D %3D

A:

Q: er-y dA, R: 0 <x< In 2, 0 < y< In 2

A: we have to solve this double integral.

Q: What is the value of - x3 + 3.4y when x = 2 and y = 5? %3D 2 18 O 20 О 21 37

A: We find the value of 12x3+3.4ywhen x=2 and y=5

Q: 2rdr Jo (r2+D²) (r2 + D²)² а TO 1

A: The expression ∫mnf(x) dx  is evaluated using the formula below .  ∫mnf(x)dx =F(n)-F(m), where, F(x)…

Q: cosh(3at) y = 3bt

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Q: (D³ + 2D*)y = 0 y(0) = -3 , y'(0) = 0 and y"(0) = 2

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Q: x² – y? = 4, x² + y? = 12 %3D

A: detailed solution is given below

Q: 2- y = xy? O y-' +x - 1 = ce* O y +x - 1 = ce*

A: Given differential equation is dydx - y = xy2

Q: 4. y" — 2y' + y = 4e¯t + 2et, where y(0) = −1, y'(0) = 2 2+

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Q: VP +y ydzdydx 2. x² +y² +z? 2 3 J0 Jo

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.