B)Get the private answer of the following equation. L(y) = t?e5t + te-t sin(2t) + t³e=2t + 7 cos t .

Q: Express the equation r = 3 cos 0- 12 sin 0 in Cartesian coordinates. (x² + y²) – 3r + 12y = 0 + y²)…

A:

Q: 2 X(+) = SIN'セ y (t) = Cos?t 9) IF dy FIND %3D

A:

Q: Find the solution of the equation cos y dy? which tends to zero as x → 0o and has the value cos y…

A:

Q: Find the general solution of the equation. xsin ydx+ xcos ydy +2 sin ydx =0

A: The solution are next step

Q: Solve the following equation for the given conditions y(0) = -1,y'(1) = 2 d²y dy + 4 dx :+ 4y = sin…

A: Given differential equation is d2ydx2+4dydx+4y=sin2x+cos2x      (1) with y(0)=-1, y'(1)=2 Auxiliary…

Q: Obtain the general solution of the following equations: sin y(x+sin y)dx+2x2cos ydy=0

A:

Q: Given dy find 36 Cos 6x y' dx sin 6x + c 6 sin 6x + c O-6 sin 6x O-36 sin 6x

A: here option a is true.

Q: Use the method of undetermined coefficlents to solve the following problem. y +8y = e-8t sin t, y(0)…

A:

Q: - 4y = e + 12t sin (2t) 2t Cze 4 + te -3t cos (2t) 4

A: Undetermined coefficient: y''+4y=e2t+12tsin(2t)Auxilliary eq ism2+4=0m=±2icomplementary function is…

Q: Given the following DE (cos 2y – 3x?y?)dx + (cos 2y – 2x sin 2y – 2xy)dy = 0 -

A:

Q: 9. y = C,eax cos(bx) + C2eax sin(bx); a and b are parameters

A: As per our guideline we are supposed to answer only first asked  question. Kindly repost other…

Q: solve the bernoulli equation dy/dx+y = y^2(sinx+cosx). and show that the answer is y(cosx+Ce^x)=1

A:

Q: set up the appropriate form of a particular solution yp, but do not determine the values of the…

A:

Q: dy 5. Solve the IVP: = cos(r+ y), y(0) = dr

A:

Q: (b) Find the complete solution (y = ye+ yp) of the following equation using undetermined…

A:

Q: solve the di¡erential equation. 17. y′ = sin^3 x cos^2 y             18. x dy - (x4 - y) dx = 0

A: 17). To solve the differential equation: y'=sin3x cos2y Solution: Given differential equation can be…

Q: Match the equation with its graph. r(t) = cos(at)i + sin(xt)j + t?k, -1 <t< 1 %3D y 4 y 2.

A: The solution of the problem is given in the next step.

Q: (c) y" + 2y-3y = 9 sin(t)

A: A detailed solution is given below

Q: Match the equation to the graph. y 2 sin 30 - 1 %3D Sn / 3n 7n 21 4.

A: y=2sin3θ-1Use the form  a sin ( b x − c ) + d  to find the variables used to find the amplitude,…

Q: Given [2r + y cos(ry)] dx +r cos(ry)dy 0. Show that the equation is exact and find its solution.

A:

Q: (cos t)y" + (sin t)y' – ty = 0,

A:

Q: (a) Solve the equation, = 4e cos 2x subject to the boundary conditions that dxdy d?u du at y = 0, dx…

A:

Q: solve for y, In - y| +C = (1n|cos(x) – 1| +c)

A:

Q: 4 x = c,eßt + cze¬2ßt sin 2t t3

A: We eliminate arbitrary constant with the help of above differential equation.

Q: Q3: B find dy/dx for the following equations : 1- y= e(3-cos4x) cot 3x 2- y =- 2x+sinx

A: Given 1)  y=e3-cos4x2)  y =cot3x2x+sinxwe have to find the derivative

Q: Find for the equation yz? – et* cos(4zx)-3y² =4 ây

A: The objective of the question is evaluate the partial derivative of z with respect to y in the given…

Q: Determine c, and c2 so that y(x) = c, sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

A: Consider the function: yx=c1sin 2x+c2cos 2x+1. Calculate c1 and c2. Given yπ8=0 and y'π8=2.   Since…

Q: In what form should the particular solu tion be sought for the equation y(1) + 2y" + y" + 2y' =…

A: Consider the equation y4+2y'''+y''+2y'=xe-2xThe characteristics equation of the homogenous equation…

Q: What are the values of and cz so that y(x) = cq sin(x) + c,cos(x) will satisfy the conditions y(0)…

A: Given y (x) = c1 cos(x) + c2 sin(x)and y(0) = 1,   y'(π) = 1

Q: Find a particular solution to y" + 16y = 16 sin(4t). Yp

A: The given differential equation is:y''+16y=16sin4t        ...............(1)The auxiliary equation…

Q: Evaluate by any applicable method. T/2 S cos sin y dy 60 120 60 None of the choices. Please refer to…

A: Topic = Integration

Q: The value of 'b' for which u(x, y) = ebx cos 5y is harmonic

A:

Q: Find the solution to the given equations: (a) y" + y' – 2y = cos(x) – 3 sin(2x), y(0) = 1, y'(0) = 2…

A:

Q: Solve the following Riccati equation dy _2 cos? x – sin² x + y² 2 cos x y1(x) = sin x dx

A:

Q: T=V3 + cos 0 is given by:

A: Trrr

Q: Given: X = 4 cos 20 and y = 2 sin 20 What is the value of d y dx? in terms of

A: We have to solve

Q: (cos 2y)-3'y de+ [{os 2y)- 2.(sin Zy) - 2xyl dy 0

A:

Q: In what form should the particular solu tion be sought for the equation y(4) + 2y"' + y'" + 2y' =…

A: We will solve it by undetermined coefficient method Let the particular integral with respect to x is…

Q: Find the solution of the D.E. below: xcos' ydx + tan ydy = 0 A y²+(tanx)²=c B x²+ (cosy)?=c © y?+…

A:

Q: Given a = 2 cos t + 26 and y = 5 sin? t dz dt dy dt ||

A: Simply take the derivative using basic concept of derivative.

Q: Given the implicitly defined function 6. cos (2*y) – y* - cos(2r) – y? dy and dr dr find at the…

A:

Q: Given: x = 4 cos 26 and y= 2 sin 26 What is the value of in terms of 6. dz O dy csc 29 dx2 -csc 20 O…

A: The solution is given below:

Q: 4. Find du for the equation 3y? – cosy = x° -

A:

Q: Find the general solution: y" + 5y' + 6y = 4e¬t cos2t + sin2t A - BI -

A: Differential equations

Q: Find the solution of the equation cos y which teds to zero as r 0o and has the valRe coS N Vwhen r=0

A:

Q: Solve for the general solution of the following equations dy d. sinx+ ( cosx) y=sin( x²)

A:

Q: Determine cı and c2 so that y(x) = c1 sin 2x + c2 cos 2x + 1 will satisfy the conditions y () = 0…

A:

Q: Find the general solution (implicit explicit) to the following equation. or et y" – 2y' + 2y =…

A: We have to find the general solution of the differential equation y''-2y'+2y=exsinx.

Q: 8 sin r at the point (, 4). e form y mx + b where

A:

Q: Given x = sin4t, y = -cos4t, then find at %3D t = 16 dx О a.3 O b. 2 O c.0 O d. 1

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.