Solve the following differential equations d²x +12dy +6x = 0 dt? dt? d x d?y 5- +16 +6y=0 dt? dt? by using Laplace transform which satisfies the initial conditions x(0)= 2, y(0) = 1, x'(0)=0 %3D and y'(0) = 0.

Q: (c) Solve the non-homogeneous second order ordinary differential equation y" + 3y' + 2y =t+1 subject…

A:

Q: Solve the differential equation using Laplace Transform. (b) y" – y" + 4y' – 4y = 10e-t, y(0) = 5,…

A: We will find out the required solution.

Q: 3. Use the Laplace transform to solve the given differential equation. x' - 2x - 4y = 4, y' + 2x +…

A:

Q: Consider the following simultaneous linear differential equations. Un even dx dy = -x + 2y, = 3y. dt…

A:

Q: Solve the following differential equations with Laplace transform method. d²x(t) dx(t) +5- dt +…

A: The Laplace transform of the function f(t) is denoted by Lf(t) or F(s), and defined as…

Q: Use the Laplace transform to solve the given differential equation subject to the indicated initial…

A:

Q: (a) Solve the following first order differential equation (without using Laplace transform): (i) = y…

A:

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

A:

Q: Solve the differential equation y" + 4y' + 5y = 0 given y (0) = 1 and y' (0) = - 4 using Laplace…

A:

Q: use the Laplace transform to solve the given system of differential equations subject to the given…

A:

Q: Solve the differential equation using the Laplace Transform, d'y 104 + 21y = e-l1t, with the initial…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: Q.2// Solve the following pair of simultaneous differential equations Using Laplace Transform: dy dt…

A: By Laplace Transformation we know that, 1. ℒ(sinat) =a2s2+a2 2. ℒ(eat) =1s-a

Q: Use the Laplace transform to solve the given differential equation subject to the indicated initial…

A:

Q: Solve the following system of the differential equations. dx +3 +y = et (1) dt dt dy --x = y dt (2)

A:

Q: Use Laplace transform to solve the following differential equation y'' − 3y' + 2y = e^−x with the…

A:

Q: B: Find the solution of the following differential equation by Laplace transform with initial…

A:

Q: Solve by using Laplace transform the partial differential equation 0² = 9. y(0,t) = 0, y(2,t) = 0,…

A:

Q: 12. y" +y'-2y = te' y(0) = 0, y'(0)=D0

A:

Q: 1. Solve the following differential equations with initial conditions by using the Laplace transform…

A:

Q: Solve the following Differential Equation using Laplace Transform. y' – 3y = e-5t y(0) = 6

A:

Q: 3. Find the solution of the following differential equation by Laplace transform with initial…

A:

Q: Consider the following differential equation d'y dy + K +y%3u dt2 dt Discuss the dynamic behavior of…

A:

Q: 4: Solve the following differential equation using Laplace transform 1. y y, +3yz, y = 4y, - 4e y(0)…

A:

Q: Solve the given differential equation using Laplace Transform (D2 – 6D + 15)y = 2 sin 3t With the…

A: Given that, y''-6y'+15y=2sin3t with initial conditions y(0)=-1,y'(0)=-4. Take the laplace transform…

Q: (B):-Using Laplace transform, solve the following differential equation -y =10-6(t-)-100 - 8(t-1)…

A: To find the solution of given differential equation first we will take the laplace transform of both…

Q: = 2x – 5y, dt = x – 2y + cos t

A:

Q: Solve the ordinary differential equation with initial conditions using Laplace transform.…

A: The given differential equation is, y''+4y'+13y=20e-t and y0=1 and y'0=3. The solution is given as…

Q: Solve the following differential equations by Laplace transform. wer (A) or (B) dx +4x 20 e6t dt at…

A:

Q: 3 Find the solution of the following Differential Equations using Laplace Transform properties; y" –…

A:

Q: 2) a) Solve the differential equation dy (t) , s¢v (t)+ 4y(t)=u(t). y(0)=0. 3- +5- dr dt j(0)= 0,…

A:

Q: Solve the given differential equation using Laplace transform method: d²y dy dt2 + 6y = e-'; given…

A:

Q: Solve the separable differential equation for u du ,би + 10t dt Use the following initial condition:…

A:

Q: 3. Find the solution of the following differential equation by Laplace transform with initial…

A: Here given as ∫0tytdt=dytdt ......1,  Since F0=1 is the initial condition then it should be y0=1.

Q: Solve the following linear differential equation using Laplace transform: y" – 4y = 0 with an…

A: First I have written some formulas of Laplace transform, just use them and easily find the required…

Q: Solve the following linear differential equation using Laplace transform y"' + y' = e* with an…

A:

Q: Find the solution of the differential equation that satisfies the given initial condition. dL=kL2…

A:

Q: Solve the given differential equation using Laplace Transform (D2 – 6D + 15)y = 2 sin 3t - With the…

A: GIVEN (D2-6D+15)y=2 sin 3twith intian condition y(0)=-1, y(0)'=-4we need to solve the equation using…

Q: ) Solve by using Laplace transform the partial differential equation a² y d'y =9 y(0,t)= 0, y(2,1)=…

A: Solution:-

Q: x' = 10x - 8 y %3D y' = 7x - 5 y %3D x(0) = 12 %3D У(0) %3D 11 Note. dx x' = dt dy y' = dt

A:

Q: 3) Solve the following differential equation using the Laplace transform method: d'y(t), dy (t) +4…

A:

Q: Use the Laplace transform to solve the given differential equation subject to the indicated initial…

A:

Q: 3. Find the solutions for the given linear systems of differential equations using Laplace…

A:

Q: Solve the given differential equation using Laplace Transform (D² – 6D + 15)y = 2 sin 3t With the…

A: Given differential equation is D2-6D+15y=2 sin 3t with initial conditions y0=-1, y'0=-4. Applying…

Q: Solve the following differential equations d²y + 64y =88(t) dt? d’y , dx ·+5x= e$t + dt? dt by using…

A: Step:-1 Ly''=s2ys -s y0 -y'0Ly' = s ys -y0Lyt = ys  ⇒L-1 ys  =ytLea t =1s-a ⇒L-11s-a=ea tLtn =…

Q: Find the solution of the following system of differential equations by Operator method or Laplace…

A:

Q: Solve the given differential equation using Laplace Transform (D² – 10D + 9)y = 5t With the initial…

A: Given differential equation is, D2-10D+9y=5t. Now, If Laplace transformation of ft is, Lft=Fs. Then,…

Q: Given a second order differential equation d°y 3 dy + 2y = 6 dt? dt where y(0)= 2 and y'(0) = 6…

A: Apply Laplace transform on both sides for the given differential equation

Q: 3- Solve the following differential equations by Laplace transform (a) x/ + 2x = 0,x(0) = 1.5 (b) x/…

A:

Q: Solve the following differential equation using Laplace transform, d²y dy dx 尝- dy dx +10y = e2x+20,…

A: