y" + 25y = 10 sin(5t). Yp =

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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.

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Q: Solve for the general solution of (cos x cos y – cot x)dx – (sin x sin y)dy = 0.

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Q: 33. sin x dx dy х 0,

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Q: Solve using Euler's Method dy dx sin(x+y) ex,y (0)-4, h-0.1 -

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

A: Given that : The differentiable equation dydx = 8 sin 4x . y = 6 when x = 0.

Q: Find a general solution to the equation y′ − 3y = e^x sin(2x).

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Q: Find the solution of the IVP: y" – 9y = sin 2t, y(0) = 0, y'(0) = 1 using method of undetermined…

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

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Q: 2y у'+ — х?у? sin x %3D

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Q: If y = (4x) sin ( 3z) then %3D dy dx (Be sure to express your answer in terms of x)

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

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

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Q: dy tan tan x = 0 dx coscos x +

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

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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: Find the general solution of cos x dy + (y sin x – 1) dx = 0

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Q: -2 cos(6t) dt J (10+4 sin(6t))²

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Q: What is the functional form of the particular solution V + y = sin(2t) + sin t

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Q: Find the general solution of y''' − y'' − y'+ y = 1 + sin x + sin 2x + ex

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Q: Find the particular solution for the given separable equation when y(0) = 3. 1 dy = ysin(2x) 1? dx

A: To find the particular solution for the given separable equation when y(0)=3

Q: Use undetermined coefficients to find the particular solution to y"+ 5y' + 4y = - 500 sin(3t) Y(t) =

A: We have to find the particular solution of  y''+5y'+4y=-500sin(3t) by using the method of…

Q: cos²x sinx dy + (y cos³x − 2)dx = 0

A: Given problem:- cos2(x) sin(x) dy+(ycos3(x) -2) dx=0

Q: ACTÍVITY 2: Differentiate the 1) y = -2 sin 2) s (t) = - WE

A: Apply the differentiation rules for the trigonometric functions to get the derivatives of the given…

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Q: Find the linear approximation to h(y)=sin(y+1) at y=0. Use the linear approximation to approximate…

A: Recall that the linear approximation of a function y=f(x) at x=a is given by y=f(a)+f'(a)(x-a) Here…

Q: What is the first step in eliminating the parameter t from the equationsx= 3 1 sin t and y = cos t -…

A: Given equations are x=3+sint,y=cost-2. To eliminate t from given equations, substitute values for t.

Q: Find the complete solution of ey sin x dy cos²x = 0 dx

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Q: dy Solve sin -1 | = x +y dx,

A: Sin-1(dy/ dx) = x+y => dy/ dx = sin(x+y).

Q: Solve the equation xcosy dy+(x+2)siny dx=0.

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Q: Find the general solution of y" – 4y' + 5y = sin (x)

A: The given differential equation is  y" - 4y' + 5y = e2xsinx

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

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Q: Find the general solution of y(4) + y" = 3t2 + 4 sin t – 2 cos t

A: Given differential equation is y(4) + y" = 3t2 + 4sin(t) - 2cos(t)

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: Find the solution of the equation azz=e cos =e * cos y d hich tends to zero as x - 0o and has the…

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Q: 2. Solve for general solution using exact method. (cos x cosy – cotx) dx – sinx siny dy = 0 %3D

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Q: (2x sinh2 + 3y cosh?) dx – 3x cosh dy = 0 |

A: Concept Used: For  y'=f(x, y)   ...(*)If f(hx, hy)=hn f(x, y)Then (*) is homogenous equation of…

Q: Find the solution of d2y/dx2 +4y=sin3xx+cos2x

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Q: у" + 4y' + Зу %3D sin (e*)

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Q: 3. Solve the DE: 1 + 2.ry? ) dx + (2ya² – cos y) dy = 0, y(1) = || - -

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Q: . Obtain in two ways the general solution of (r+ sine – cose ) dr+r(sine + cose ) de = 0

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Q: Solve by Bernoulli's Equation 2. sin y(x + siny)dx + 2x?cos y dy =0

A: We find the solution by Bernoulli’s Equation.

Q: Find a particular solution by inspection of d²y dx2 +y = -7+e* + cos 2x – 10 sin x

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the general solution of the equation cos x cos y dy – sin x sin y dx = 0

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Q: 8. (sin°(5y)dy

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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: find the general solution of dy/dx + y = 2 sin x.

A: Now comparing with Now integrating factor is,

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: 6y' = y*sinx У (0) — 1

A: