# Question   Dear expert ,Please answer this Numerical methods for physicists question completely .Please explain the problem stepwise and  give explanations so that we can understand .Thank you we value your time and efforts.​​​​​​​ 4. Consider the initial value problem (IVP) $\dddot{x}+3 \ddot{x}+2 \dot{x}=0, x(0)=3, \dot{x}(0)=-2, \ddot{x}(0)=5,$ where $$0 \leq t \leq 10$$. (a) Write down the above IVP as a system of coupled first-order differential equations. [4 marks] (b) Write a MATLAB $${ }^{\circledR}$$ program using the ODE solver ode45 to solve the above IVP with a uniform step size of $$0.01$$. [8 marks]

CTZUC3 The Asker · Physics

Dear expert ,Please answer this Numerical methods for physicists question completely .Please explain the problem stepwise and  give explanations so that we can understand .Thank you we value your time and efforts.​​​​​​​

Transcribed Image Text: 4. Consider the initial value problem (IVP) $\dddot{x}+3 \ddot{x}+2 \dot{x}=0, x(0)=3, \dot{x}(0)=-2, \ddot{x}(0)=5,$ where $$0 \leq t \leq 10$$. (a) Write down the above IVP as a system of coupled first-order differential equations. [4 marks] (b) Write a MATLAB $${ }^{\circledR}$$ program using the ODE solver ode45 to solve the above IVP with a uniform step size of $$0.01$$. [8 marks]
More
Transcribed Image Text: 4. Consider the initial value problem (IVP) $\dddot{x}+3 \ddot{x}+2 \dot{x}=0, x(0)=3, \dot{x}(0)=-2, \ddot{x}(0)=5,$ where $$0 \leq t \leq 10$$. (a) Write down the above IVP as a system of coupled first-order differential equations. [4 marks] (b) Write a MATLAB $${ }^{\circledR}$$ program using the ODE solver ode45 to solve the above IVP with a uniform step size of $$0.01$$. [8 marks]
Community Answer
LLPSFY

&#12304;General guidance&#12305;The answer provided below has been developed in a clear step by step manner.Step1/1We can solve this differential equation using Laplace transform.Apply the Laplace transform to both sides, (use the Laplace table to see the Laplace transform of various functions)The belowThe image gives the calculation procedure for the question.https://drive.google.com/drive/fo ... See the full answer