(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

A:

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: {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: Answer: y = (2/x) + (c/x)ex

A: Given

Q: п/4 sec z dz

A: By using integration formula, we calculate the given integral.

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: ) ور شم( موم 2 4-x 2 2 4-x 2 x++y¯+z° e - dz dy dx -2

A: To evaluate the below integral. ∫−22∫04−x2∫04−x2−y2e−x2+y2+z23/2dz dy dx

Q: Solve the followi ing

A: As per our guidelines we are supposed to answer only one question. Please repost another question as…

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

A:

Q: : )-+(÷), zw= (C) dx 1 et %3D dt 1 (: :)-+(-), -= (C) dx dt 1

A: Given dxdt=0110 x +ete-t Here let take A= 0110A-λI=-λ11-λ=0λ2-1=0λ=±1 Hence the eigen vector for 1…

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

A:

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"

A:

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+)

A:

Q: Q5) Use the Chain Rule to express dy /dx in terms of x and y: y = csc t and x = sec-1t

A:

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?

A:

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…