Ordinary Differential Equations

I'd like something to compare my answer to before submission.

Consider the following system:̇x = ẏy = −x + x3 + aya) (1 pts) Find the fixed points of the system.b) (1.25 pts) For which values of a is the system not conservative? Why?c) (1 pts) Show that for the...

Need help with the attached problem. 

Undetermined coefficient method. I did the work but I'm not sure if it's correct. 

(a) Seek power series solution of the given differential equation about the given x_0. Find the recurrence relation (b) Find the first four terms in each of two solutions y1 and y2.

Please only answer questions 1,2,4 and 6. 

The question is asking you to find the equation of the displacement for the object (door+buffer) after the collision. You can find the displacement equation x(t) by first finding the equation of motio...

I have my general solution but the initial condition is $y(0)=y_0$. How do I know what $y_0$ is?

Attached file has 4 questions to answer. I have attempted these but would appreciate seeing someone else attempt them before I submit. Must show all working please.

Solve the ordinary differential equation $\frac{d^{2}y }{dx^{2} } =y$  for y as a function of x. (Note that this is equivalent to y" = y.)Solve the partial differential equation $ \frac{∂^{2} f}{∂x∂y}...

Use Gaussian Quadrature of order 5 to approximate$\int_{2}^{6} \frac4{x-1} \;\mathrm{d}x $ Please solve this ODE using the method in this resource: https://www.dam.brown.edu/people/alcyew/handouts/GLq...

Hello, I'm not looking for any solutions here but rather I’m having difficulty figuring out how I should properly approach this question… Using a Gaussian Quadrature of order 5 to approximate$\int_{2}...

Answer all questions with all work shown.

Answer all 5 questions with all the work shown.

I just need the one question on first page of the attached pdf solved. Please clearly list and justify each step in words with proper mathematical terminology and notations. Please double check the st...

Answer all questions on first page (questions 1-5) with all steps shown. Page 319 from the textbook, referenced in question 3, is displayed on the other pages.For each question, clearly explain why yo...

Answer assignment questions 8, 9, and 10 with all steps shown.Also include (alongside the work or on a different sheet of paper) an explanation of each step you did to get to the final answer and why,...

Answer the assignment questions with all steps shown. Also include (alongside the work or on a different sheet of paper) an explanation of each step you did to get to the final answer and why, using p...

Prove that the system of ODEs $y_1'=-y_1^3 + y_2^5$ $y_2'=-y_1y_2^4-y_2^3$ is asymptotically stable in $(0,0)$.

We have the system of ODEs $y_1'= y_2$ $y_2'=-y_2-\sin(y_1)$. Decide for each of the following functions whether it is a Lyapunov-function of $(0,0)$ or not: $V(y_1,y_2)= y_1^2+y_2^2$. $V(y_1,y_2)= \f...

We have the system of ODEs $y_1'=y_2-y_1 \cdot f((y_1,y_2)^T)$ $y_2'=-y_1-y_2 \cdot f((y_1,y_2)^T)$, where $f \in C^1(\mathbb{R}^2, \mathbb{R})$. Prove the following statement: If $f((y_1,y_2)^T)>0...

Find all real solutions of the linear equation $y''+\frac{4}{x}y'-\frac{10}{x^2}y =0$ on the interval $(0, \infty)$ by using the substitution $y(x)=z(\ln(x))$.    

Find the $\textbf{general}$ solution of $y'= \left (\begin{matrix} 1 & 1 & 1 \\ -1 & 0 & 1 \\ 1 & 1 & 0 \end{matrix} \right ) \cdot y$  and a solution with the initial value  ...

We have   $y'=f(x,y)$  with $f : \mathbb{R}^2 \rightarrow \mathbb{R}^2, \left (\begin{array}{c} y_1 \\ y_2 \end{array} \right ) \mapsto \left (\begin{array}{c} g(y_1) \\ h(y_1) y_2 \end{array} \right...

Find a factor Q(t,y) that makes this equation exact, please include some steps