Solve the following initial value problem using the undetermined coefficients method: d'y dt2 + y = 8 cos(2x) – 4 sin(x); with y =-1, y(1) Choose the correct answer among those proposed: A. y =(e + er)- 8x B. y (2x-n)cos(x)-sin(x)-cos(2x) C. y(1-e*) - * -41 С. у x + 25 D. y = )e#* + !r* +* + 2cos(2x)- stn(2x) 64

Q: Find the solution of y" + 9y' = 162 sin(9t) + 1296 cos(9t) %3D with y(0) = 5 and y' (0) = 9. %3D y =

A:

Q: Given y(x) = c₁e²x + c₂e* + 2 sinx, find the values for ₁ and ₂ so that the conditions y(0) = 0 and…

A:

Q: 3. Solve for y in the equation y = e* sin x + e* cos x - y +c

A: the given equation is y = ex sinx + ex cosx - y +c

Q: 1. If x'y" + xy' + (x². 4 - -y=0 Y=x sinx , and y= y,v. Which of the following x>0 equations…

A: Solution:    Given:                  x2 y"+ xy' +(x2 14) y =0, x.o                 y1 = x-12…

Q: Show that (1-)dy+(cos xsin x-sy")dr =0 is an exact equation. Hence, find its general solution. Hint:…

A:

Q: = Complete the following truth table. Use T for true and F for false. You may add more columns, but…

A:

Q: Find the general solutions (implicit or explicit) to the following equations. (a) y' = e3x-2y + x²…

A: First order ordinary differential equation.

Q: Show that an implicit solution of 2x sin?(y) dx – (x² + 16) cos(y) dy = 0 is given by In(x? + 16) +…

A:

Q: Solve: (cos x) · (dy/dx) + y sin x = 2x cos2 x, y(Tt/4) = (-15/2-n2)/32.

A: The given differential equation can be written as :            dydx +ytanx = 2xcosx So, the…

Q: Solve (x + sin(y))dx + x cos(y)dy = 0 and find the solution passing through (2,7)

A: Given: We have to solve the given differential equation and find the solution passing through

Q: Find the solution of y" + 3y = 126 sin(3t) + 54 cos(3t) with y(0) = 2 and y' (0) = 7.

A:

Q: an initial investment of 1500 thousand dol ollars at the end of each of the next two qua The…

A: Given: Initial Investment=$1500000 Further investment=$250000 (Quarterly) Operating cost=$120000…

Q: cos(t) dt 2/3sqrt(x+5)^5-10(x+5)^(1/2) +C (5 sin(t) + 9)2

A:

Q: What is the general solution of the given equation, cos(x + y) + 2x + (cos(x + y) + 4y)y' = 0 OA.…

A:

Q: Find the solution of with y(0) 3 and y' (0) = 8. y = y" + 3y = 108 sin(3t) + 36 cos(3t)

A: see below the answer and explanation

Q: Find y = 223 [tan(3r+1)] 2° + ry – y5 = 8x2 = (x + 3)² (x² – 2x) -

A: The Product Rule : The Product Rule says that the derivative of a product of two functions is the…

Q: 2. verify that each of the following equations has the indicated solution : • y" +4y =0 y=ae2x+bxe2x

A: By Bartleby policy I have to solve only first one as these 2 are unrelated problems. First problem:…

Q: Find the solution of y" + 4y = 160 sin(4t) + 224 cos(4t) with y(0) = 3 and y' (0) = 2. y =

A:

Q: Determine a suitable form for Y(t) if the method of undetermined coefficients is to be used. y" -…

A:

Q: 47. Show that y = sin(tan-x+ C) is the general solution of y' = /1 – y²/(1+x²). Then use the…

A:

Q: Question 2 Find the solution to the DE. (y-x+xycotx) dx + xdy=0 xysinx=C+ sinx - xcosx Oy=(c +…

A: Concept: For a differential equation of the form P(x,y)dx+Q(x,y)dy=0 The differential equation is…

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: (10) y "+10y "+34y '+ 40y

A: Introduction: A differential equation is an equation that contains the derivative of an unknown…

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

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.