Solve the solution of the DE of the Doomsday Equation: dy ky' dt ,(1+c)

Q: Find the solution of the differential equation that satisfies the given initial condit du dt 2t +…

A: The given differential equation:                                          dudt=2t+sec2(t)2u…

Q: : Solve the differential equation by using Laplace Transformation hod? у" — 4y' + Зу %3 0 у (0) %3D…

A: Taking Laplace Transform in both direction:

Q: Example 64. Solve the simultaneous equations: dx -y3 e', dt dy +x = sin t, given x (0) = 1, y (0) =…

A: Given dxdt - y = et    --- (1)dydt+x = sin t   ---(2)with  x(0) = 1, y(0) = 0

Q: Construct an autonomous first-order differential equation dy/dx = f(y) whose phase portrait is…

A: From the figure, the critical points are 1, 3 and 5. Thus, f(y) should contain powers of (y-1),…

Q: Find the particular solution of the differential equation that satisfies the initial condition(s).

A: Given: f'(x)=6x f(0)=8 Integrate the equation. ∫f'(x)=∫6xf(x)=6x22+Cf(x)=3x2+C

Q: Solve the differential equations by applying Laplace transform. i. y' + y = 8(t – 1), y(0) = 2,

A: We will find out the required solution.

Q: y" + 4y = 0 ; y(0) = 2, y'(0) = 2

A:

Q: Solve the final solution for the differential equation with initial values: y(0) = 2 & y'(0) = 6.…

A:

Q: 2 dy + y? = ty. dt

A:

Q: solve the wave differential equation  utt-c^uxx = 0; u(x,0)=log(1+x^2),ut(x,0)=2

A:

Q: 1. (x* + ху? — у)dx + (у' +x?у+х)dy %3D 0

A:

Q: Solve the final solution for the differential equation with initial values: y(0) = 2 & y'(0) =6. Use…

A: The given initial value problem is                                             y''-3y'+2y=6 ;…

Q: dy Write down a differential equation of the form dt solutions all approach y = as t- →8. y' = = 78…

A:

Q: In the given equation , use a computer algebra system to graph the slope field for the differential…

A:

Q: Q:- solve the differential equation by Laplace transform : y" – 3y' + 2y = e3t %3D Where the initial…

A:

Q: test whether the differential equations are exact and solve those that are. 2Y dy 0 dt+-

A:

Q: Determine the order of the differential equation. (dy/dt)^2+7 dy/dt+9y=3t

A:

Q: find the solution of following differential equation using Laplace transformation. y" + 3y + 2y = ex…

A:

Q: Solve the differential equation. dz + 4et + z = 0 dt %3D - In(#|) z = C+

A:

Q: Solve the differential equation that satisfies the given initial condition: dy xe",where y(2) = 0 dx…

A: We first separate the variables and then integrate  C= integrating constant

Q: t sec 0 de dt Oet?

A:

Q: Solve the differential equation dY AY dt for (; 1). vm - () 3 Y(0) = A =

A:

Q: Use an Integrating Factor to solve the differential equation.

A:

Q: test whether the differential equations are exact and solve those that are. y dt +t dy 0

A:

Q: Find the solution to the differential equation dz = 2te?z dt at passes through the origin.

A:

Q: dy 1. + ty? = 0 dt

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: The integrating factor of the differential equation dy +(1+ dx is xe O

A:

Q: Solve the Following Bernoulli Equation dy = y – y² – ya | dt Show ALL Workings

A:

Q: 2) y" + y = e¬2.sint ve y(0) = y'(0) = 0, Solve the differential equation with the initial condition…

A:

Q: Find the IVP for the differential equation X y' -3xy'+ 68y=0, that satisfies the initial conelitions…

A:

Q: y" - 3y' + 2y = 6

A:

Q: Find the general solution of the differential equation and check the result by differentiation. dy =…

A:

Q: Solve the differential equation y" +4y' +4y 6e", y(0) =-2, y'(0)=8. using Laplace transform

A: Given differential equation:y''+4y'+4y=6e-t ; y0=-2 and y'0=8To find: solution by using the laplace…

Q: Use Laplace transforms to solve the differential equation ,, Y +6y' + 13y = 0, given y(0) = 3 and y'…

A:

Q: Solve the Bernoulli equation for y. dy 2y + y*. dt Use the following initial condition: y(0) = 1.

A: We need to solve the Bernoulli equation for y. To solve given differential equation first using…

Q: dy 3D е* + 2, у(1) — 1 dx

A: We will solve the given problem by using differential equation by intial problem .

Q: Transform into Bernoullis' form the differential equation ry' +y - r*y ly = ry? dz + zy = ry? dz dy…

A:

Q: Solve the fallowing Partial differential equation. 2. (Da + Da Dy - 6 Dt ) u = yoS x |

A: The given partial differential equation(pde) is a second-order homogenous linear pde. A linear pde…

Q: dy = xe', y(0) = 0 dx %3D

A: dydx=xey⇒dyey=x dx⇒e-y dy=x dx⇒∫e-y dy=∫x dx⇒-e-y=x22+C⇒e-y=-x22-C⇒-y=ln -x22-C⇒y=-ln -x22-C

Q: 6y = -12 y (0) = 1, y' (0) =4. y" (0) = -2 %3D 3.) at + 4 dt

A: Take laplace on both sides of the given equation and then Use-…

Q: Solve using separable differential equations dx 3xt? dt

A:

Q: Solve the differential equation using Laplace transformation y" – 2y' + 3y = 2t²e3t where y'(0) =…

A:

Q: | f(t)f(t – t)dr = 6t³ 0,

A: According to the definition of Laplace transform Lf(t)=∫0∞e-stf(t)dt. If F(s) is the Laplace…

Q: Find the solution of the differential equation that satisfies the given initial condition. 2t +…

A: The given differential equation is dudt=2t+sec2(t)2u⇒2u du=2t+sec2(t) dt ..................... (1)

Q: Use Laplace transforms to solve the differential equation y' + 2 y = 10 e3t , if y(0) = 6

A: The given equation is: y'+2y=10e3t,y(0)=6...(1) Taking Laplace transform on both sides of equation…

Q: Consider the second-order differential equation d?y + 25y = 2.5 sin(6t). dt? Find the Particular…

A:

Q: dy ト+e dx

A: Calculus

Q: dL kL² In t, L(1) = –1 dt

A: Given differential equation is  dLdt=kL2lnt,        L1=-1