1) Find solutions to the following equa t ions having the specified initial value   a) x" + 4x = 0 x(O) = 1 x(O)' = 0   b) x" - 3x' + 2x = 0 x(l) = 0 x(l)' = - 1

Q: 4. Solve the forced undamped mass-spring problem z" + 9x = sin(3t), x(0) = 2, x' (0) = 0. Graph the…

A: in the given problem we have to solve the give forced undamped mass spring problem…

Q: Find the solution of the following Differential Equations 1) 4y"+y 0, y(0) = 2, y'(0) = 0.

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: 4x(1-x)y"+y'+8y=0 Solve Gauss' hypergeometric differential equation

A: Let Its general solution is given by where,

Q: a. y" = xy' - x

A: This is a problem related to differential equation. Please follow the procedure given below. As per…

Q: Qs: Solve the fallow ing differential equations 2.

A:

Q: 5) y" - y = ex + x² 6) y" - y' - 6y = e-* - 7) y" - 2y' + y = x³ ex. 7 cos x

A: Given that: y''-y=ex+x2y''-2y'+y=x3ex. The solution of the differential equation is obtained by…

Q: Find the solution of the following Differential Equations 1) ydx+ xdy 0 2) (xdy- ydx)/x = 0

A: Find your answer below

Q: 2) If we know that y,(x) = e2* is the solution for the equation (2) xy" + (2x – 1)y' – 2y = 0 (2) a)…

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Q: 3. Solve the differential equation (a) r" - 91 = 5e²t (d) I" - I' = 8e²t (g) I" - I' = 6 sint (b) r"…

A:

Q: Find the solution of the following Differential Equations 2) (xdy- ydx)/x 0 4) 2x In(y)dx+ y'r dy 0…

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Q: 3) Consider the differential equation ty" + ay' = f(t) i) Find the general solution of equation (3)…

A:

Q: 1) Consider the differential equation dr =r' = 2x + cos²t, r(0) = ro- dt i) Solve the differential…

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

Q: 6) Solve the differential equation zy" +2(1 – 2) y +(x – 2) y = 2e", if y, = e" is known as a…

A: The given differential equation is:…

Q: What form should you guess for a particular solution for the following differential equations? A)…

A: Solution. (A) Given the differential equation y" -6y'-7y = x2 +3x Hear the auxiliary equation is m2…

Q: Find the solution of the following Differential Equations 2) y"+2y'+y x 4) y"+y=-30sin(4x)

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Q: y" + a1(x)y = 4 sec²(8x)

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Q: 1) For the differential equation = e-(2 + cos(x)) dy i) Find the solution satisfying y(0) = 3. Find…

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Q: In this problem you will solve the non-homogeneous differential equation y" + 4y = sec²(2x) Let Cj…

A: We solve given DE by variation of Parameter Method.

Q: 3. Solve the initial value problems y" + 2y + 2y = sin 3x; y(0) = 2, y'(0) = 0 y(3) + y = x + e*;…

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Q: 5. The equation y" +y-2y = 2 is called a differential equation because it involves an unknown…

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Q: 4) dy dx = sec(x + y) 2x-2y+1 5) y' = x-y 6) y' 2л —Зу+4 x+y+2 7) xy^y' = x³ + y³

A: According to our guidelines, we can answer only first question.  Substitute x+y=t, then from…

Q: he general solutions of the following ntia a) y(4) – y – 15 = 0 b) x+ y = x* Jy c) y"" + y = 2 sin x…

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Q: (2)Solve the following initial valne Problemss- a) Xy'+Y=0(r2) = -2), b) e*y'=2(x+1)y° (ro) -V6) ,…

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Q: 4.Calculate the differential equation y''= 3x + y2 + y + y', y (0) = 2, y (1) = 4 by shoot-ing /…

A: Given that the differential equation is  y''=3x+y2+y+y'; y(0)=2, y(1)=4 Also given that h=1/3 we…

Q: Find the solution of the following Differential Equations 1) y'- y= 3 2) y'+2.xy = 0

A: "Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: The curve given by y=x+3 sin (x) is a solution of the differential equation: O a) y' = x + (y – x)…

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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.