b) Solve the differential equation dx² + 4y = e".

Q: Solve the differential equation x²y" - y = e-3*.

A:

Q: Solve the differential equation (x+y)y'-y=0

A:

Q: Solve the Linear first Order Differential Equation xdy - sin dx

A: See the attachment

Q: (D² - 3D + 2)y = 2e-* +8

A:

Q: 5. у" + у' — 2у 3D 0 ||

A:

Q: 3. у'-4у+3у3D 2 сos x + 4sin x

A:

Q: Solve the differential equation f -e = 2ey by separation of variables.

A: In this question, concept of separation of variables is used. Seperation of Variables The approach…

Q: Solve the Differential Equation (D² + a²)y = Tanax by the method of Variation of Parameters.

A:

Q: $2. x" – 4x' +3x =te".

A: Given that x''-4x'+3x=tet To find the general solution :

Q: 4. x"+4x' +4x =0.

A: Let, x = emt be a trial solution. So, x' = memt  &, x" = m²emt So, the characteristic equation…

Q: solve the for the general solution of the differential equation( linear homologous equation): (D2 +…

A: We have to solve the differential equation: D2+2D-1y=0 The given equation is in symbolic form where,…

Q: Q-2. Form the first-order differential equation of e = sinx

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Q: A solution of the differential equation 2 y"

A:

Q: Solve the differential equation (x2y-2xy2)dx=(x3-3x2y)dy

A:

Q: (D² - 1)y= 2 1+ex

A:

Q: Determine the general solution of the differential equation

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Q: (x4 - 2x34 + x²y?) dx +(2x"- 2x3y) dy = 0 %3D

A:

Q: Solve the differential equation 1.) dy = (y²xe^3-3x²y)dx

A: Please see the below picture for detailed solution.

Q: Solve

A:

Q: Solve the differential equation y''''+y''=3x2+sinx-2cosx a) what is the complementary solution b)…

A: We have to solve the differential equation y'''' + y'' = 3x2 + sinx - 2cosx a) Complementary…

Q: 5) Solve the differential equation with appropriate method. xdy-ydx-√(x2 + y2) dx=0   Show…

A: We have to solve the differential equation xdy-ydx-x2-y2dx=0.

Q: Solve the differential equation,  x⁴ y' = -x³y - csc (xy)

A: Given, x4y' = -x3y -csc(xy)⇒y' = -x3y -csc(xy)x4                    1substituting y =ux , u is a…

Q: Solve the differential equation y" – 2y' + y = ° *| *

A: solve the differential equationy11-2y1+y=exx .....(i)

Q: The differential equation x*y) - x y"- 5 y = 0 is a Euler-Cauchy equation. :Select one True False

A: The objective is to determine whether the given statement is true or false. Given differential…

Q: *- 2- 2 - - 2 = 0 dx dx

A: The solution is given below-

Q: Solve the differential equation. y' = 4x – y %3D

A: Let v=4x-y Differentiating both sides we get: ddx(v)=ddx(4x-y)v'=4-y'y'=4-v'

Q: Solution of the differential equation 3y +2x dx O represents a family %3D

A: Introduction :

Q: Find the general solution of the differential equation

A: We have given differential equation drds=49r We have to find general solution of differenial…

Q: Solve the differential equation: xy'-2x2y= y ln y

A:

Q: Solve the differential equation Integrating Factor by Linear Equations:  y' = 1 -2y cot2x

A: To Solve the differential equation   Integrating Factor by Linear Equations:    y' = 1 -2y cot2x

Q: Solve the differential equation y""+y" = 3x² + sin x - 2 cos x What is the particular solution?

A: We have to find the particular solution.

Q: Solve the differential equation xy' - 3y = 2x° In x. The solution is y = (Type an expression.)

A:

Q: 5) Solve the Partial Differential Equation- a2z 2 dx²

A: Given partial differential equation is, Zxx-2ztt=0         ........1 It can be written as,…

Q: (2x³ – 3x²y + y³)ª = 2x3 – 6x²y + 3xy? dx

A:

Q: Solve the differential equation and initial condition and verify that your answer satisfies both the…

A: Given,           y'=2xy2           y0=13

Q: у + 2ху 3D х, у(0) — — 2

A:

Q: Solve the differential equation. y' + 3xe" = 0

A: The given differential equation is: y'+3xey=0 To solve the differential equation.

Q: yu+y=be" +bsinne +bsine.

A: Given DE is y”+y=6ex+6sinx solve the DE

Q: Solve the differential equation by undetemined coefficients y" – y' = -3

A: Solution- Given y''-y'=-3 ⇒dy2dx2-dydx=-3-----(1) dydx=m ⇒m2-m=0⇒m(m-1)=0m=0, m-1=0≠m=1 Distinct…

Q: dy sec Cx*) dx ×ス - る× (x-3)2

A: The given differential equation is an ordinary first order linear differential equation. Consider…

Q: 30. x" + 10x =0.

A: We have to find General Solution of the given Differential equation.

Q: The solution of the differential equation

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Q: -lo I3+ 5 %3D dt

A:

Q: 4. Solve the differential equation y" + 5y = - csc V5x CSC

A:

Q: Solve the differential equation: 29 - y + 1=0

A: We have given the differential equation2y"-y'2=-1So, the auxilary equation will…

Q: Solve the differential equation by an appropriate method. d³y, dy dx3 tanx dx

A: Find the complementary function and particular Integral of the given equation. Its general solution…

Q: -2у y+2xyy' = e" y 'y'

A: Please see the answer in step 2

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.