(5) Under what Conditions is (ax+by) dx + (KX+LY)dy=o exact? selve the eXact equation,Ca, b,k, L Cunstant) • (ANS.5): b=k,ax+2kxy +LY=C•

Q: d²y + 4y = x² sin 2x dx2

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Q: 5) Solve the Non-linear second ODE: d²y + 3 x² y dx? y? = x² ) (dy %3D

A: Given: Non-linear second order differential equation is 3 x2 y d2ydx2+y2=x2(dydx)2

Q: XY x + Vy² + 1 ) dx dy = 0 - Vy?+1

A: Topic  -  differential equation

Q: Find DF of fcxiy)=x²e° at the point (-2,0)-

A: Given function is fx,y=x2ey. We have to find the ∇f at the point -2,0. We know that ∇f=∂f∂xi+∂f∂yj…

Q: {G) = -2x+5 firid f(2)

A: To find: The value of f1. Given: The function is fx=-2x+54. Calculation: Substitute x=1 in…

Q: S √ + (25 +4z²)(z³ + 1)¹² dz

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Q: - 2- Solve: (2x +1) a.) dx3 +2y 3e* dx %3D dx2 + 6(2x+ 1)+4y = (2x+1) [t= In(2x+ 1)] %!

A: According to our guidelines we can answer only one question and rest can be reposted.

Q: : Solve the equations3; 1. D² – 6D + 9)Y = 7e3* %3D

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

Q: use Euter me thed to solve y's 2-24

A: Let us consider the given function y'=f(x,y), y(x0)=y0 Solving using the Euler method  Then the…

Q: Determine for which value of m the function $(x) = x" is a solution to the given equation. d²y dy…

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Q: The general solution of y" - 4y + 8y = 0 is: Select one: а. ce?"cos2t + cze?'sin2t b. -6t + Cze2t C.…

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Q: L{t sin t cos t} = 2s (A) (s²+4)2 -2s (B) (s²+4)² (C) 14) (s²+4)² -8 (s²+4)2 (E) (s²+4)²

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Q: Find the general solution of the equation y" – 2y' + 5y F0 Do not need to show your work, just give…

A: First we find the auxiliary equation and then we find the general solution of the given homogeneous…

Q: - 3x³)dy – (2y³ – x²y)dx -

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Q: Ive by the method of variation of parameters (without using formulae): D°y + 2Dy + y = e* /r°.

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Q: 1 -dxdy =? (4+x² + y²)°

A: Here we will use change of variable in double integration

Q: y" tý = -6xx 8 y²-y = et (² siux + 4 cos x) 9) ý - Ý x y" + y ² -4 y² - 4y = 3 = ³x - 4x-6.

A: Since you have posted multiple questions,  as per our guidelines we are supposed to be answered only…

Q: TT Q3(a)- P.T B(m, n) = 2 [? sin2m-10cos2n-10 d0. b. Also verify part (a) with counter example.

A: We have to prove that  βm,n=2∫0π2sin2m-1θ cos2n-1θdθ And also verify this with counter example

Q: Let f(x) = - then f'(- 1) = (x + 2)2"

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Q: (d) : 2x² – 8x – 13 dx x² – 5x – 6 2.

A: As per company rules we can answer only first question and rest can be reposted

Q: Find general solution. y" + 4y = 5 sec ² (2+)

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Q: (22 + 3?) dx – xy dy = 0 O 22 In () = y² 2a In() = 3 (금) %3D 22 In(을) %3D P O a² In ( ) = y?

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Q: Q NO3)IF y=Jsinx + Vsinx + Vsinx + . then show that(2y-1) = cosx .And Also Find dx (5vcosx) dx

A: Our objective is to find the derivative of above functions.

Q: Solve (1+y)dx + x y dy = 0 A)- B)+e D)

A: The given equation is 1+y2dx+xydy=0 Rewrite the equation as 1+y2dx=-xydydxx+ydy1+y2=0dxx+ydy1+y2=0…

Q: sec2 z dz, any path from 7/4 to Ti/4

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Q: Solve item 1 only. Find the general solution. Note: Use y" and y' as forms of terms, not dy and dx…

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Q: OFind the inlagral of : S(725(フスーヴxりー23x +4ズ)(1-4で

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

Q: 5) /2xy =1 dx ans: +c 3

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Q: yo2y'tuy (2) +29+ S: A sinuk

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Q: Q2) Determine the general solution: 1- (x²+y²) dx = 2xy dy

A: