Solve the following initial value problem: y" – 6y' + 13y = 0, y(2) =4 y'(1) = 9 %3D -

Q: y(VIn2) O a. 2 O b. 3

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Q: Convert y " (f) + (1 – t) y' (t) + e¯' y (t) = t – 5t; y (0) =- 3; y' (0) = 4 into an in tegral…

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Q: Find f'(x). f(x) = (1 – 7x)10

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Q: Solve the following IVP y"-y'+y/4=0, y(0)=2, y'(0)=1/3

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Q: Find a general solution of y'" = (- 50 – 50 i /3) y. ... y(x) = C, e +c2 e-

A: The given differential equation is y''=-50-50i3y Demoiver's theorem for fractional power  If rcos…

Q: Solve the IvP y'+aty%3D1

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Q: "+3 v' = 0: v(0) = 3. v'(0) = 6. %3D %3|

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Q: Show that the function f(1) = 5e²' satisfies y" – 3y' + 2y = 0, y(0) = 5, y'(0) = 10. %3D

A: The function ft=5e2t & the differential equation y''-3y'+2y=0 & the conditions y0=5,…

Q: S(y* - y-3)dy

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Q: Solve y'' + 9y = 8(t – 2), y(0) = y'(0) = 0 y(t) = for t 2

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Q: Solve the initial value problem (t2 – 5)x' – 2tx = -2t(t² – 5), x(2) = 7.

A: Given differential equation is t2−5x'−2tx=−2tt2−5......1 and x2=7. We have to find the solution of…

Q: 1 Separate variables to find a solution a. yy' +36x=0 b. y'=1+4y², y(1) = 0

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Q: 2. (D2 – 4)y = 0 when y(0) = 0, y' = 3

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Q: Find Y(s) in the form p(s) SIMPLIFY COMPLETELY. 9(s) * y" – 9y = e³t y(0) = 1 y'(0) = -1 %D

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Q: 2. yy = 4.x, y(1) = –3

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Q: y'

A: The function is given as : y'''-y''-2y'=0. To find the general solution of the function , The…

Q: Y = C1e* + C2ex + C3e2x where y(0) -D 0, y (0) %— 1, у"(0) — 2

A: The differential equation is: y=c1e-x+c2ex+c3e2x At x =0, y = 0, so c1+c2+c3=0....(1) At x = 0,…

Q: x' = -2x + 4y y'= 4x - 5y x (0) = 1 y(0) = 3 %3D Δt - 0.1 Use the Euler method with a time step of…

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Q: Solve (2 3 5 or t < 3 y'' + 6y' + 25y y(0) = y'(0) = 0 %D Give the solution for 3 <t < 5 y(t) =

A: For the given condition, the given differential equation in symbolic form is (D2+6D+25)y=2 The roots…

Q: Q-1:B: Solve the initial value problem d?y + 4y = 8x2 ,y(0) = -3,y'(0) = 0 %3D %3D dx2

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Q: 1. Solve the following equation y" – ky' = 0 given that y(0) = 2, y'(0) = k %3D

A: Please refer to the image below

Q: Solve the problem y' = x²y², y(0) h = 0. 1. Select the correct answer. = 1 numerically for y(0. 2)…

A: Euler's Method is used

Q: 10. use "Bernoull's Equation" method dy -y= ey! dx

A: The given problem is to solve the Ordinary differential equation using Bernoulli equation method, we…

Q: (10) Solve the given BVP by using Green's function: ; (ii) y" – y/ = e2; y(0) = 0, y(1) = 0

A: Given differential equation is: y''-y'=e2x y(0)=0y(1)=0 Green function in equation is given by:…

Q: 3. Solve y'" + 6 y' + 9 y = 0, y(0) = 5, y'(0) = - 8 %3D %3D y (t)

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Q: (c) y" – y' = t², y(0) = y'(0) = 0.

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Q: 4. Find the complete solution of 2x³y' = y(y² + 3x²) %3D

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Q: 2. y" + y' = cscx %3D

A: 2. we have  y''+y'=cscx  first find C.F m2+m=0m(m+1)=0m=0,-1y(x)=c1e0x+c2e-x=c1+c2e-x

Q: 5 solve the 1UP: y% 4y(2)+ 3y'= Y1)=e+ % ,uG) = et %

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Q: (1– 1)y' – y² +x²y+2x = 0, Y1 = -x² %3D

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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.