4) Find Yp, using D-operator, where Yp (e). %3D (D+1) (D-2)

Q: D Exponential Shifting Theorem 4 (D° + 4D°-3D - 18)4=24x°e-3× t 4D²-3D - 18)y = 24 x°e¯*

A:

Q: Find the general solution of each ff Higher-order DE using Reduction of Order  1. (2D2 + 3D -2)y=0

A:

Q: 1. y" - y' - 2y = e by D- %3D operator method

A: We have to find CF and PI

Q: Find d2y/dx2 implicitly in terms of x and y.

A: Implicit differentiation involves the treatment of one of the variables as a function of another and…

Q: Find Hhe (imet 3. 3. im +y²+xy

A: Explanation of the answer is as follows

Q: b) - 2y dy

A: Integrate the following.      ∫y4-2y-4y-2dy

Q: dz Find - if z = (9x + 5y)°. dy

A: we can find the derivative as below

Q: 12 - y+ ] - dy = |+C

A:

Q: y'(t) = In(y- 3) %3D

A:

Q: 3. Sy? e2y dy

A:

Q: Z. WY = %3D

A:

Q: What is the solution of the given ODE xy' + y = Vx

A: Given: xy'+y=x

Q: Q:2: a) Find implicitly, if y²cosy +x² = 2xy

A:

Q: What is the transformed equation for y = x2 when it has been translated down 7 units? %3D Oy-(x-7)2…

A: To find the translation of function y=x^2

Q: (e) Yk+1 +Yk = 1/k(k+1),

A: Given, yk+1+yk=1kk+1Substitute:yk+1=y'yk=yEquation formed is:y'+y=1kk+1A first order separable ODE…

Q: Why is e^x^3 using the product rule instead of the chain rule??

A:

Q: Example 13: If Jf(x)dx =-3, )dr=9, and f(x)dx 5, find %3D

A: given∫4-6f(x)dx=-3,∫37f(x)dx=9∫47f(x)dx=5to find∫-63f(x)2-3dx

Q: 2 Find the Cerivative o3 a) y°(x+2)= c3

A:

Q: Evaluate (D^2 - 3D + 2)y = (1 + e^-x)^-1.

A:

Q: Calculate ∂ω/∂z for ω=e-2xe (z^2y)

A:

Q: EX. Evaluate the JJ(X*+2xy+y") dydx when step size of x = 0-2 and step Size of y=o.5?

A: Given: ∫01∫02x2+2xy+y2dydx with a step size of x=0.2 and y=0.5.

Q: If x2 z2 + y² + xz3 = 3, then dz at the point (1, 1, 1) is: O b. Ос. - 3 d. - 3 Ое. f.

A:

Q: S(2 + e2*)³dx

A:

Q: Consider the following IVP: y' = e; y(0) = 2

A:

Q: O': Find the general yy' – 2y² = e²

A: A first order Bernoulli ordinary differential equation is of the form dydx+pxy=qxyn Where p(x) and…

Q: 2 da x² – 8x + 17 Integrate: + C

A:

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

A:

Q: S 9a – 3d = 3 %3D -За + d %3D -1 d = -1

A:

Q: (D² – 3D – 4)y = 0 is ° y = C,e** + C,e* " y = C,e** + C,e* 4х 4x -X -4x ° y = C,e** + C,e* y = C,e*…

A:

Q: Consider z=e (*3+y2) Evaluate dx2 O (6r2+ 3x)e (*3+y2) (9x4+6x)e (x³+y²) (6x4+ 9x) e (x³+y²)

A: Topic = Derivative

Q: 6) Find most general antiderivative of the fxn. a) f(6) = x5+2x²-1 X' B) 4(1) - 2 +30*

A:

Q: 3 2x y°e*dydx

A: To Evaluate the integral given below:-I=∫02∫04[y3e2x]dy dx-(i)Computing the definite…

Q: Calculate ∂ω/∂z for ω=e -2xe((z^2)y)

A: While calculating partial derivative ∂ω/∂z, all other variable except z will be considered as…

Q: a) Let y" + xy' + y = 0 be given. Why does the approach y(x) := e^× does not work?

A:

Q: (у-3) dy y2-6y+1

A: To evaluate the integral: ∫(y-3)y2-6y+1dy Solution: ∫(y-3)y2-6y+1dy…

Q: The discriminant of ax2 + bx + c = 0 is defined by_________.

A: The given equation is ax2+bx+c=0.

Q: 2 c2x-4 ( dydx 2у - 1) Q2. Evaluate the double integral x + 1

A: In this question we have to find the double integration.

Q: Í (x)dx, iff(x) = Vx -k +1;k-15x <k, k = 1, 2,.n.

A:

Q: 48xyz < (3x + 2y)(y+ z)(3x + 2z) for every x, y, z E [0, +∞[.

A:

Q: 3 -dp 72 + x2 Integrate: + C

A:

Q: ral of the d D- 1)y is

A:

Q: (a) In e7 (b) eln 2 %3D (c) eln v3 %3D Preview (d) In e5

A:

Q: %3D18 SK+y%= {x-zy=9 11

A: Given query is to find the solution of the system.

Q: (c) 부3D . Yk+1 k+1 Yk k

A:

Q: f Lan 2X e *3 of +sec2X Pinel dy o

A:

Q: 2 4 Mx(t) = -e+ 3t e' + e" + %3D 3 15

A: Given: Mxt=13et+415e3t+215e4t+415e5t

Q: What is the discriminant of the PDE?    4d2/dy2=-3du/dx-4u

A: the discriminant of the PDE is :

Q: 6. Differentiate y with respect to x using A-method. x-3 a. y = X b. у %3D V4x + 3

A:

Q: y = (2x + 1)v2x+1

A:

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…

A: