Solve the given symbolic initial value problem. y''-y'-6y=5*δ(t−1)+e^(2t)​      y(0)=0.     y'(0)=5

Q: 5y' + xy = x2 + 5

A: We solve the differential equation by finding Integrating factor method. For the standard first…

Q: y''' -3y'' + 3y' -y = (e^x)(x+1) find the general solutions of this diff eq

A: Given differential equation is y'''−3y''+3y'−y=exx+1 Write the auxiliary equation  m3−3m2+3m−1=0…

Q: tx' 3 - - (³ 4) X X = C1 (1) +02 10 + ()

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Q: y''-2y'-y=8e^t    find the particular solution

A: In this question we will find the solution of the differential equations.

Q: Solve x*y"- 2x(1+x)y'+2(1+x)y= x'

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Q: Solve 2y'' - 5y' - 25y = 0, y(0) = 0, y’(0) = = y(t) = - 37.5

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Q: Solve y" +5y' = (2x+1)e" -5x

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Q: Find y'' in y = x2 (x3 - 1)5

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Q: Find an expression for h'(x).  h(x) = 2 f (2x + 1)

A: Given equation - hx = 2f2x+1    .........(1)

Q: Find y'. In(5x) y = 4x y' =

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Q: y = (x + y – 1)².

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Q: solve y''-y'=xex  using undetermined coefficient. The characteristic equation will be r2-r=0

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Q: 3 + 2x g(x) %3D 5 - 8x

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Q: which is the corred differential equation of the relation y = x + be* + ce* after elimination of the…

A: Solution: Given that

Q: solve  w' + ((2w)/x) = x5,       w(0) = 1 what is w(1)

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Q: Solve the given initial-value problem. X(t) -2 2 *-(1) · () * - () X' = + X(0) 3 4 2

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Q: Solve y'' + y' — 6y = 0, y(0) = 8, y'(0) y(t) = = - 9

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Q: 4) Solve (xe + ye" )dx+(xe" +e' )dy = 0

A: The differential equation is xe-y+ye-ydx+xe-y+eydy=0 Write it as: e-yx+ydx+x+e2ydy=0x+ydx+x+e2ydy=0…

Q: Find y'' in y = (1 + 1/x)3

A: We first expand the given expression first.

Q: The total number of reported cases of an illness in a large city tt days after the start of an…

A: Given the logistic differential equation is: y'=15600y1400-y…1 The standard form of a logistic…

Q: 8) y'+y=17 sin(2t), y(0) =-1.

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Q: Solve (1-x³) y' -2(1+x) y = y5/2 Bernouilli

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Q: Solve xy' = y +1

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Q: Equation in (a) becomes the non-homogenous equation, y'' − 2y' +y = e^2x . Solve the particular…

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Q: Consider the differential equation y'' + 6y' +9y = 0.

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Q: Solve for the differential equation of the given function y = C1x + Cze* by applying elimination of…

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Q: Find y'. In(5x) y = 7x

A: SOME RESULTS:     IF y= f(u) and u=g(x) then,  dydx=dydududx.      ddxuv=vdudx-udvdxv2,v is non…

Q: Find y'. y = [In(x5 + 3)]2 y' =

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Q: Differentiate. g(x) = 7x-1 4x+7 g'(x) = + x3

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Q: xeʼlin (2x+1)-2e ln(2x+2)=0

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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.