3 1f y=/xL5x²–3. x_3x²+¥x- 3, X25x²-3 huw that dy 24 ||

Q: 6x2+7y2=C satisfies 6x+7yy' given the inital condition y=4 when x=6 what is C.

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Q: Obtain the general solution. (D² + 1)y= secx O y= C,cosx+ C2sinx + xsinx - cosxln|cosx| O y= C,cosx…

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Q: 9. Solve d²x dt² + 4x + 5y = 1²; d²y dt² + 5x + 4y = t +1.

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Q: d²y 5. If y = 4sinx + x²cosx + 4x then find dx2

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Q: compute ∫_D 2ydx+3xdy, where D is described by 0≤x≤1, 0≤y≤1

A: Green's Theorem: Let C be a positive oriented, smooth, simple closed curve. Let D be the region…

Q: Find the general cowtion of the die. y9) + ya) - 24 =-e (9+67x+17 x²) + (861nax - o cosex) „(2).…

A: The given differential equation is , y(3)+y(2)-2y = -e3x(9+67x+17x2) +…

Q: f(t) = te3t cosh 4t s²-6s+7 s2-6s-7 А. (s2-6s+25)2 С. C. (s2-6s-25)2 s2-6s+25 В. (s2-6s-7)2 s2…

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Q: 2 X+y +Z=lo Gouss eleminahin 3 X+ 2Y4 32=18 X +uy+ 9Z= 16 ماركة العرض من قبال

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

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Q: Find y' by implicit dif ferentiation for 2y³+4x² –y = x6 . 6x5- 8x y '=- 6y2 – 1 A 6r5 + 8x B 6y2– 1…

A: Given, 2y3+4x2-y =x6 We have to find y' by using the implicit differentiation.

Q: 31. If 9x² = y(y – 3)², show that (y + 1)² ds - dy². 4y

A: We know that Given Firstly, we find dx in terms of dy

Q: 2. x + 5y +15 z + 35 w + 70t = 0 X + Y + z + w +t =1 X + 2y + 3z + 4w + 5t = 0 2x + 6y + 12z + 20w +…

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Q: X1, X2 2 0 12. Minimise Z = 60x1 + 80x2 bo Subject to 20x +30x2 2 900 40x1 +30x2 2 1,200 X1, X220 LO…

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Q: 2. X + 5y + 15 z + 35 w + 70t = 0 x + y + z + w + t = 1 X + 2y + 3z + 4w + 5t = 0 2x + 6y + 12z +…

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Q: 2. x + 5y + 15 z + 35 w + 70t = 0 X + y + z + W + t = 1 X + 2y + 3z + 4w + 5t = 0 2x + 6y + 12z +…

A: We have to find the solution of the linear system.

Q: IF y = u+ + 3u2 & u = 2x 64x3 + 30x 8x(8x2 – 3) الخيار رقم 1 خيار 3 Find dy dx 8x(8x2 + 3) 8x(8x3 +…

A: We can find the derivative as below.

Q: f(x, y) = In(4x² - y) %3D

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Q: 7. f (1, y) = z + y subject to z² – zy + y² = 1

A: Let h(x, y)=x2-xy+y2. Then we have ∇h(x, y) = (2x-y, 2y-x) and we also have ∇f(x, y)=(1, 1). Let the…

Q: 8. = In(3x² – 2y + 4z³); x = 1/2, y = t²/3, z = 1=2 w

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Q: Xxy-Z = Gauss eleminatin %3D 2X -y42=5 -x +2y+23 or

A: We have to solve given problem:

Q: max z = 2x + 8y %3D s.t 3x + 9y 12 х, у > 0

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Q: (b) If z = 9t²e 4, find dz dt 4

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: Show that Inx dx = -/Zn². x3/4(1+ x)

A: The given integral is: ∫0∞lnxx341+xdx

Q: А. X+dy =3 2x -3ÿ =-8 B. x tay +2 =-2 X tdy +Z=-2 -2メ-39-2 = dx +4y tQz==4 ミ9

A: As per the company rule, we are supposed to solve the first three subparts of a multi-parts problem.…

Q: (2) Find dt2 if y = x2 + 3x -7 and x 2t + 1 | 2

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

Q: S (x+Sy+wz ) dzoly dz 2 3x X-つ

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Q: 3 If y=/xL5x²_36 x²_3x²+Yx-12 (3 14 shuw that dy 24 dx4

A: firstly simplifying these expressions then , use the concept of differentiation

Q: :Q3 Classify PDEs below и ди y2 и + и = ue 5x — - ду

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Q: f(t) = te3t cosh 4t s2-6s-7 А. (s2-6s+25)2 s2-6s+7 С. (s2-6s-25)2 s2-6s+25 3. (s2-6s-7)2 s2-6s-25 D.…

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Q: 3. Obt nin the parh cular folu tion 9. xdx - ydx + 3x dy +ydy = 0 ; wun x - 5,4= -:

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

Q: Find of z = 2x° 5xy" + x¯ y dy2 -10ху + 3x? у? = -10y + 6xy²

A: To find ∂2z∂y2 of z = 2x3-5xy2+x2y3

Q: Find dw. If w=2x3 +3x2 y-6y² 3 dw=(x2+6xy) dx+(3x2 -y) dy Ob dw= (6x2 +6xy) dx+ (3x2 – 12y) dy

A: This question is taken from the partial differentiation in which we have to total derivative of the…

Q: 14 (3 3 1f y=/xL5x²–36 x15x²-36 X23x²+¥x-12 show that dy dx4 24

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Q: j. Min Z = 12x, + 8x, subject to: 4x, + 2x, 2 24 2x, + 2x, 2 10 2x, < 8 X,, X2 20

A: To solve the Linear programming problem using the graphical method  Consider the constraints as…

Q: 14I hox)= x)-0, whese fCn=2 and fとい=8,

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Q: 9 2. If fS(x)dx= 37 and g(x)dx=16, = 16, find [2f(x)+3g(x) ]dx- %3D 0.

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Q: 2. § (5z² - 7z + 3) dz from z = 2 to z = 1

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Q: dy 3y y torh(x) + 2

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Q: 3 If y=/x²5x²_36 x²_3x²+¥x-12 | shuw that dy dx4 24

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Q: yz 4. II »z dr dy dz Jo

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Q: A x² B --x-In Ix+11+ C x² 2 -x+ In lx+11+ C 5x²=² dx x+1 C x² D x² +x-In Ix+11+ C +x+ In lx+11+ C

A: The given integral,              ∫x2-2x+1dx

Q: 3 9-r22 1 dy dz dr 9-r2 0_æ²_22 (x² + y² + z²)1/2

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Q: 2/3 If y = xl/3 + 2 dy then |z */0 =-8 dr

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Q: Differentiate x²y3 - y2-6x=0 with respect tox. A 3x²y2-2y −6+2ху 3 2х3у2-2y - 6 6-2xy3 3ху2+у В С D…

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Q: Evaulate: 2 1 pr+y (x)dzdydx 0.

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Q: 3. 1 S [(2x - 4y)dydx 31 1 -1

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Q: 11. Find y'if y = 2x + Vx* – 9x+3

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Q: dy 6. S: y3-2y2

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Q: 6 4 for f(x, y) 3 3x у - 4x'у". 5 3 Verify that дх ду ду дх df 4 5 18y x - 20y°x of 5 3 4. 2 18x°y -…

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Q: What is L[y] if y = u3(t) (t- 3)2? %3D L[y] = e3s . - 3 O Lly) = e3s. 2 L[y] = e-3s. 2 O Lly] = e-3s…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.