FIMD dY IF x= AMD Y= U 1tu3

Q: 14 Lys 9 -25+ dy = Vy

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Q: /1- (z² + y²) dz dy dæ ) Evaluate

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Q: 1) dt2 +k²x = 0 2) ax² 3) (x² + y²)dx + 2xydy = 0

A: "Since we are entitled to answer up to 3 sub-parts, we will answer the first three  as you have not…

Q: 2 Solve + Iny) daz + 플dy= 0

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Q: Bernoulli dy + xy = dx y # 0 уз

A: The objective is to find the general solution to the given differential equation

Q: Find dy if y2T+4+ In(x+2)= xy3 dx y - 2Vx+4 2yvx+4 -3xy 2x+4 2yvx+ 4 y -2 2yvx +4 - 3xy- Vx +4 2yvx…

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Q: Compute if df = 2 and dx du dx = 6.

A: It is given that,

Q: 4. Find dy/dx og y = xsinx

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: 25y2-4 dy 415 S. 2/5

A: ∫254525y2-4y dy Put, y=25secθ Differentiating with respect to θ, we get ⇒dydθ=25secθ tanθ⇒dy=25secθ…

Q: 1-Vy dy Vy 4

A: We need to find the given integral.

Q: Solve dy ху = 1+x +y+ xy dx y = In|x(1 + y)|+c Option 1 In(y + 1) = In(x) – Option 2 y = x + In|x(1+…

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Q: 1 11z Evaluate ſ dz [ dx

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Q: Non Homo (D4 − 1)y = 0

A: Differential equations

Q: , 4cosx dx dy

A: First draw the region of integration. Then, use the region of integration to change the order .…

Q: 4 2 S[(x) dy dz 0 0

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Q: If y = e Oe3 Oe 3x X² O 2e3 O 3e³ then dy dx at x = 1 is

A: To find derivative of given function at x=1

Q: dey こてxニコッン alx

A: We have to find :- d2y/d2x= ?

Q: du _ dv dy dx If f(z) =z²+z - ,2

A: Take z= X+iY and proceed

Q: If y = 2u – 3(u² – 3u)* 3 (u² – 3u) and U = Vx –1. Find | | dy when x = dx 17

A: It is given that y=2u3-3u2-3u2 and u=x-1.

Q: 1 10z Evaluate dz dz S dy. 0.

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Q: dy 1 andy 3x? + 1 if- dx Find- atx = -1. dt dt 1 6 -6 ||

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Q: 2 Evaluate S S dx dy dz.

A: Evaluating the definite integral

Q: dy Find dæ if y = In(x² + 9y²). dy dx

A: We can find the derivative as below.

Q: 1(cotx) dy dx = 1 ctan 10n а. 44 157 b.- 44 20n с. 44 1-A d. 2

A: topic:-  application of integration

Q: 7. [(4cosx+3sin.x)*dx 8. ſcos°(3y)dy 1 (у-5)3 v – 5)³ 9. -dy 7 y3 (3 – 2 cscx)² 10. cotx

A: Integrate above function.

Q: 1. Determine for y(s) if y(0)=3, y'(0)=-2 and y"(0)=7 dy dy dy +5 + 6- =D0 dt dt3 dt2

A: We have given differential equation, d3ydt3 + 5d2ydt2 + 6dydt = 0  It's Auxiliary equation is given…

Q: 3. f Arctany dy 4. fx(2x - 1)'dx 5. fycsc²ycoty dy 6. fxsin4xcos4x dx

A: The given integrals are;  5) y csc2y coty 6) x sin4x cos4x.

Q: 7. If S PCx) dx = 14 and %3D S.I find 6. fCx)dx

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Q: xdx – Va² – x² dy = 0

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Q: Show that y +4 dy = 4 In lyl – 3 In |y + 1| + C y2 + y

A: To Prove:  ∫y+4y2+ydy=4 lny-3 lny+1+C

Q: Inx+1 dy will be dx If y = then 2x3 – 3x' (2x³ – 3x) +1) –- (In x + 1)(6x? – 3) А. (2x³ – 3x)² (2x3…

A: Using derivative rule of (u/v),

Q: First order linear in (y-x+xycotx)dx+xdy=0

A: The given problem is to find the solution for the given first order linear differential equation.…

Q: 13) xdy- ydx 0 15) ycos(x)dx+3sin(x)dy 0

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Q: In Prob. 1-38. Find dy/dx.

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Q: exey (2xe + )dx + ( ) dy - ex ر ول

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: dy 1+y+1

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Q: 3 [[ 3x² + 4y dy dx = [[ 3x² + 4y' dx dy 4y³ We have Select one: True False

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Q: Find formulas for dy and Ay if y = 8x – 4. | dy Ay =

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Q: 5) Use improved Euler method to find y(2) if y(1)=2 for dy xy!/3 %3D dx take h=0.5

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Q: dy = 7 if x* – In(xy) + 32x+y² dx

A: To determine dy/dx for the below equation. x4−lnxy+32x+y2=7

Q: Find d if y = In(x³/x + 9). dx

A: Known fact: ddxfgx=f'gx g'xddxfg=fg'+gf'

Q: 3. Evaluato S S (2x + y)dx dy. 14-1 1-gt %3D %3D ダー1 %3D 6. %3D %3D 3 3 1.3 = %3D %3D

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Q: 1 y2e- dy 7 صواب ihi

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Q: 5. ydx - (x +3y')dy = 0 Ans. x = 6y In C

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Q: 1. S 2xe2*dx

A: Given that,   Using integration by part

Q: S(Vcos x + sin x)´dx

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Q: 1-x2 So Si S dz dy dx 0. 0.

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Q: Evaluate ex+y dx dy In8 1-y y=0x=0 O e-In2 eln 8-7 025

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