y"+y = sin x, use Method I

Q: If y = tan-1 xy and (x = 2, y = 3) y will be equal to?

A: See the attachment

Q: 19-x Evaluate ,* sin(x + y*) dy dx

A:

Q: fex Sin X %3D

A: According to guidelines we solve one question (2).

Q: The appropriate trigonometric substitution for * dx is V3x-x 3 3 X ==+ sin 0 2 2 sec 0 4 2 O Option…

A:

Q: Calcula te Y Sin X dX ,n=Lo by SimPSon rule

A:

Q: How do i differentiate y=e^sin2x + sin(e^2x) step by step?

A: Differentiate y = e^sin2x+sin(e^2x) with respect to x.

Q: Solve y y (x, 0) = 3 sin 2n x, y (0, t) = 0 =y (1, t); 0 0. %3D

A:

Q: tanx dydx 1. 1+ y? 2cscx sin y(sin x)²r'drdxdy 2.

A:

Q: (2) Find it -ソ= x(lue) 2- Y=lu(Cosx )

A:

Q: sin(x+y) = y + 2cosx

A: We have to find dydx.                                   sinx+y=y+2cosx

Q: The general solution of y 'tanx sin2y = sin?x + sin?y is

A:

Q: Find the general solution to y" +y = x sinx

A: We are given second order non homogeneous linear differential equation with constant coefficients.…

Q: solve using the appropriate method. y' + yx= sin x

A:

Q: Use Substitution method: y' tan x sin2y= sin^2 x+cos^2 y

A:

Q: Differentiate y = (1+ sin* (æ²)) °. 3 8.

A:

Q: Show that if y = V1 + sin x then sin x

A: We can solve it by doing derivative and make the proof.

Q: y" + y = cos x ; when x = 0, y = 0, y' =

A: I am going to solve the given problem by using some simple calculus to get the required result.

Q: y = Ceax cos(bx) + C2eax sin(bx); a and b are parameters y = Ce2x cos(3x) + Cze2* sin(3x)

A:

Q: 2x – sin y y' = x cos y

A:

Q: (÷) – -, y (1) = 1 y tan-! y'= '() x tan-!

A: We will find out the required solution.

Q: cosy -y sin(y +2)dzdxdy

A: Given integration can be simplified as

Q: y = cev2z + Cze + C3 cos(v2x) + C4 sin(/2x) + Czev3z + Cge + c7 cos(/3x) + Cg sin(/3x)?

A:

Q: coth*(sin 3z) 12) zp- V1- ? 3z tanh

A: Integration of given function

Q: sin(6y) sin(8y) dy.

A: Topic - integration

Q: 9.) y(4) + 2y" +y = x² sinx

A:

Q: When evaluating ∫x sin x dx, explain how letting u = sin x and dv = x dx makes the solution more…

A: ∫x sinx dx

Q: Find the general solution for y' = sec x + y tan x %3D

A:

Q: y'' + 3y' + 2y = sin ex

A:

Q: I3Jsin'x cos x dx .6,

A:

Q: Evaluate and simplify y'. y = V1 - x* + x² sin-'x?

A: Given that y=1-x4+x2sin-1x2.

Q: sin x = x (1 + tan y). Find and provide solution for dx/dy

A:

Q: sec' x dx 1- tar

A: We use Trigonometry substitution method

Q: coth“ (sin 3z) -dz /1– tanh² 3z 12)

A:

Q: 23. cos (3z + 4) dz 25. sec2 (3x + 2) dx

A: A

Q: Solve sin - () 2 dy = x + y

A: We need to use substitution method to solve this differential equation

Q: IFFERENTIAL EQUATION plve using variation of parameters p² + 1)y = tan?x

A: Variation parameter method

Q: Find y' of sin(x+y)=x+y

A: Given,              sin(x+y)=x+y

Q: sin y cos(cos y)dy

A: We have to evaluate the integral: ∫sin y coscos ydy In this case we will use substitution method. So…

Q: If y = tan-1 xy and (x = 2, y = 3) %3D %3D y will be equal to?

A: Given: y=tan-1xy To find y' at x=2 and y=3. Solution: Chain rule of differentiation states that:…

Q: * sin x 2. SS y dydx ans: 4

A: Using Double Integration

Q: Find y' and y". y = cos(x?) y' - -sin (x²) ( 2x) y" =

A:

Q: The value that will satisfy potentia. function p is x + y sin x None = In (x +y %3D

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: e of y = -3 sin x + 5? (I Vミー

A:

Q: Se²x+lnx² sin x² dx = +fe²x co 2x cos x² dx

A:

Q: coth“(sin 3z) 12) Vi- dz /1– tanh² 3z

A: The given integral: This can be written as, To evaluate the integral:

Q: 2. Solve the DE: -+secx(y-2sec³x+2 sec² x tan x) + y cotx=0 dx

A:

Q: find δƒ/δx and δƒ/δy. ƒ(x, y) = sin2 (x - 3y)

A: Given: fx,y=sin2x-3y  To find: ∂f∂x,∂f∂y

Q: -y' y x = sin + %3D

A:

Q: Calculate tan x ( sec“ x ) dx using u-substitution with: (i) u = tan x (ii) u = sec x

A: I have stated the used formulas in the solution.

Q: x = 4u sin v, y = 2u cos v.

A: