Determine ?? using undetermined coefficients: 1. y'' + y' + y = 2xex

Q: solve using the appropriate method. y' + (tan x)y = cos2 x, y(π) = 2

A:

Q: Given 2(dy/dx)+3y=sin⁡2x,y(0)=6 and using undetermined coefficient method: What is the complementary…

A: We have to find  the complementary solution, yc using undetermined coefficient method.

Q: Find the particular solution : y" + y' + 16y = sin4x 1 (а) Ур — — 4sin4x (b) Ур 3sin4x --cos4x 1 (c)…

A: Correct option: C The detailed answer is listed below, kindly do like it if you find my answer is…

Q: Consider the following IVP: y" +y' = -cos x; y(0) = a, y'(0) = b Find the general solution. A y(x) =…

A:

Q: 2 sin? 11. y = 3x 2x2 12. y = cos°V2x – 1 3. 13. у %3D Vtan(х?)

A: As we know that; The chain rule: fgx'=f'gx·g'x The Quotient rule: fg'=f'·g-g'·fg2 The Power rule:…

Q: (3х' - 4х- 3) x* – x' +x² – -* dy = cos ydx – - 1- sin? y y

A:

Q: Topic: Variable Separable and Homogenouse D.E. I need particular solution for 4

A: We have to solve

Q: I Eliminate the arbitrary constants -2x 2X Y = C,e cos 2× + Ge sin 3X

A:

Q: y" + y = 3x sin x

A:

Q: Find the general solution of y′−y=sin x + cos 2x using variety of parameters

A: Given that: y'-y=sinx+cos2x To compare the given differential equation with standard form of…

Q: Obtain the general solution to the equation dy dr 2+x COS x, y(0) = 2. 5.

A:

Q: Suppose that 3x² - y² = t² and y=tsin 0. Find (27). = sin e 0 X = 0 and

A: Given 3x2-y2=t2 and y=tsinθ

Q: 1) If y = (x − a)√2ax - x² + a² sin−¹(*—ª),t ), then y'= 2√2ax-x² a is constant.

A: As per instructions, Here is the answer of question 1

Q: Find the General and Particular solution of = 8 sin 4x ; y = 6 when x = 0 %3D dx

A: Since you have asked multiple questions in a single request, we would be answering only the first…

Q: RFind dy/dx in terms of x and y if cos²(8y) + sin²(8y) = y+4. |

A: Given query is to find the derivative of the given expression. Pp

Q: 1) x² sin(y') + xe2 – cos(z?) = 3y– 6z + 8 cos(z?) = 3y – 6z + 8 %3D -

A: Given; x2siny3+xe3z-cosz2=3y-6z+8 Now differentiate partially with respect to x we get,…

Q: 5. ) Using the Method of Undetermined Coefficients, give an appropriate guess for y,. y(4) + 9y" =…

A:

Q: 1 Cos(2x)dx 0. (i) Using composite Trapezoidal rule with n = 2, 4

A: As per the policy of bartleby the provisions is to solve only one question at a time So I am solving…

Q: 2. The suitable Trignometric substitution that solves fx(x-2) dx is (x-1)=sin 0 x-1)3sec0 (x-1)=tan…

A: We can find the answer as below.

Q: azz = e2x-y + cos(-3x + 2y) + 3x, дхду Given that az where əx 5x2 – sin (3x) when y = 0, and Z =…

A:

Q: I. Eliminate the arbitrary constants -3x y= C, e sin2x + - 3x Cze cos 2x

A:

Q: 10. Given that 2y- sin 2x =0 and y = 0 when x 0, then y?= %3D %3D dx B. 1-cos 2x C.-2 cos 2x A.…

A:

Q: Verify y = 4 cos(2x) + 6 sin(2x) is a solution to y" = -4y.

A:

Q: 1. . Use the method of characteristics to solve the first order equation Uz – 2uy with u(x, x) =…

A:

Q: 3. Determine a root of the equation sin(x) + 3 cos(x)-2-0 Using the Secant method correct to five…

A:

Q: 2 cos(플x-지) =D v2 TO

A: Given trigonometric equation is:  2 cosπ2x-π=2 We have to solve for x.

Q: dz Find x? sin(2y – 5z) =1+y cos(6zx) -

A: This is partial derivative so differentiate it as normal differentiation of z with respect to y…

Q: 4. Find the solution of the equation = e * cos y dy? which tends to zero as x → 0o and has the value…

A:

Q: 18) * x-sin 2x ; find y" y y" cos 2x y = 7 %3D Option 3 O Option 1 y" sin 2x

A: First we find out first derivative with respect to x then we find out 2nd derivative with respect to…

Q: 3. x = 2 cos(3t) – 4 sin(3t) and y = 3 tan(6t) at t = 2

A:

Q: Find the solution. dy X-+ 2y = dx sin x y(2) = 1 A cy = (3 – cos 2x – tanx)/x? B x = (2 + cor2 –…

A:

Q: 4. What is the form of y, given (D² + 9)y = x + tanx? A. Yp = V,sinx + vzcosx B. Y, = v, sin3x +…

A:

Q: æ' = y – 5 sin (3t); y/ = -4x + 17 cos (3t) , ift = n, x = 7; y = -4

A:

Q: 2- Calculate y": y = 5x2 Sin (3z) - 2x Cos (5x)

A:

Q: 5. Find y', if y = 2cosx sin2x – sinx cos2x d'y dx? 1-cos4x 6. if y = 1+cos4x du

A: Topic:- derivatives

Q: y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

A:

Q: 5 dx 3 dx, x> Find V25x-9 0 sin 13x+c -13x+C InV1+9x +3x +c 5x 25x2-9 in 3 + C 3 In 5x 25x2-9 + C 3.…

A:

Q: 2. Solve (sin y – 3x² + 5)dx + (y +x cos y)dy = 0. (Test for exactness and solve)

A:

Q: Obtain the GENERAL SOLUTION tan'ydy = sin xdx xdx-Sa²-x² dy =0 y'exyz

A:

Q: 3.) Solve the equation using discontinuous function: y" + 9y = cos(2t) – U37(t)cos(2t) , y(0) = 0,…

A: We will find out the required solution.

Q: +3x2. Find dy/dx if: (y)² = sin5(cos³(- -)) 2 %3D

A: Given: (y)2=sin5cos3x7+3x22 ----(1) To find: dydx Let u=x7+3x22 , v=cos3u w=sin5v Now equation (1)…

Q: Differentiate y= e*cos (x2): y' = A -e*sin(x²) e(cos(x²) – 2 xsin(x²)) e*cos(x?) – 2 xsin(x²) D -2…

A:

Q: 1. f(x) = In 5x 2. у %3D 103х Final Answer: Final Answer: 3. y = sin(e3×) 4. у %3 cos 2x (e**-1)…

A:

Q: Solve the initial value DE y - ytanz = sinx, y(o) = 1 5-Cos 2x 5-Cos 3x 5-Cos 2x Cos 2x A) y = B) y…

A:

Q: A particular solution for y +2y +y=1-cosX

A:

Q: Find the General and Particular solution of = 8 sin 4x ; y= 6 when x = 0 dx Find the General and…

A: The given equations,1.dydx=8 sin4x ; y=6 when x=02. dydx=4y ; y=3 when x=0

Q: Show that an implicit solution of 2x sin?(y) dx - (x2 + 17) cos(y) dy = 0 is given by In(x? + 17) +…

A:

Q: 44. First verify by substitution that y (x) =x=1/2 cosx is one solution (for x > 0) of Bessel's…

A:

Q: Determine the general solution of (cos(x)cos(y)-cot(x))dx=(sin(x)sin(y))dy

A: Given: cos(x)cos(y)-cot(x)dx=sin(x)sin(y)dy