Consider the following. x' = 4x + y y' = −2x + 2y,   X(0) = (−1, 2) The general solution is (x(t), y(t)) = (c1e3t[-(1/2)cos(t)+(1/2)sin(t), cos(t)] + c2e3t[-(1/2)cos(t)-(1/2)sin(t), sin(t)] Find the solution satisfying the given initial condition?

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

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

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Q: If f(x) = cos(2x) then find II f (t|4)

A: Given query is to find the Indicated derivative.

Q: Find the general solution of y"+y = cos(t) (a) Using undetermined coefficients (b) Using variation…

A: Find the general solution of (a) Using undetermined coefficients.(b) Using variation of parameters.

Q: The solution of 1y"+ y' = 0, y (0) = 0, /(0) =1 /(0) = 1 %3D is y(a) = %3D (A) cos a (B) sin a (C)…

A: The solution of a differential equation must satisfy the differential equation. Check the options…

Q: y" + 2y' = 4x – 5 cos(x).

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Q: Find f. a) f '''(x) = cos(x),    f(0) = 7,    f '(0) = 8,    f ''(0) = 8   b) A particle is moving…

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Q: y" (t) - y(t) = 4 cos(t) ;y(0) +0 , y'(0)=1.

A: The objective of the question is to solve the given second order differential equation with the…

Q: 3-(cos x)y' =yCv-1) sin x.

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Q: Use variation of parameters to find a particular solution, given the solutions y 1, 2 of the…

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Q: 1 – s2 S

A: we have to differentiate y  y=cos-1s+s1-s2

Q: The solution to the equation is * y'(x)- 2y'(x)+ y(x)-cos(x) slad Ja sin(x) - y(x) =c,e" +e,xe"…

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Q: where O O O y(t) = (f-cost)-(1)[(1 − 6) - cos(t = 6)] + 6 sint +4 cost - sint) ([(-6)-sin(t-6)] + 6…

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Q: y(x) =- 10 n +2x' +8x' + 48) +qe* +c, sin(x)+ c, cos(x)

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Q: he • (D'+D)y(x) =x The general solution to the equation y(x) =-G cos(x)+c, sin(x)-x* + 3x² +q 4 y(x)…

A: find complementary and particular solution to find the general solution.

Q: Which of the following functions is a solution of x²y" + xy' - y = 0. y(x) = x2 y(x) = x y(x) = e*…

A: Given differential equation

Q: The solution to the equation is y'(x)-2y'(x)+y(x)-cos(x) slad

A: Let us consider the given differential equation y''+ay'+by=Q(x) To solve the equation  Take the…

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: How can I find the particular solution of y''+36y=cos(6x)

A: How can I find the particular solution of y''+36y=cos(6x)

Q: s to find a particular sy1, y2 of the s(x))y'+(sin(x) - cos(x)) y = e 2 = e-* cos(x)

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Q: Use variation of parameters to find a particular solution, given the solutions y1, Y2 of the…

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Q: ind the solution of with y(0) 2 and y/(0) = 5. = = y" + 4y = 96 sin(4t) + 96 cos(4t)

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

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Q: (1+x)y' + y = cosx; y(0) = 1

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Q: IV. y-y=sin x+cos 2x +e

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Q: Find the general solution dy + cos(x)y = cos(x) dx O y = 1+ ke-2 sin(x) O y² = 2 sin(x) + c y =…

A: Given differential equation is dydx+cosxy=cosx........1. We have to find the general solution of the…

Q: z(x) 1+x² You need to find the formula for y'(x) first, then evaluate y'(x) at x = (c) Let y(x) = =…

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Q: Solve the equation y" +4y= S(t-4π), y(0) = 1/2, y'(0)=0 a. )= = cos(2t) + sin(2(t − 4π)µ(t − 4π)

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Q: y" + 3y' + 2y = e* (t2 + 1) sin(2x) + 3e- cos x + 4e"

A: Answer

Q: Solve y" + 2y + 2y = e cos(x) with y(0) = y'(0) = 1.

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Q: 4. Consider a3(x)y"" + a2(x)y" + a₁(x)y' = 0 (a) What's one trivial solution? (b) Suppose the…

A: Please see the attachment

Q: Find the general solution of the x²y" + xy' − y = 3x, x‡0;

A: *By Bartleby policy I have to solve only first one as these are all unrelated problems.These are all…

Q: (b) _x²y″ − 2xy' + (x²+2)y = 0, given solution y₁ = x sin x -

A: (b) The differential equation is given as , x2y''-2xy'+x2+2y=0              .....1

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.