prove that (0,0), (1,-1),(-1,1) are solutions of the system of non linear equations equations given as

Question : prove that (0,0), (1,-1),(-1,1) are solutions of the system of non linear equations equations given as x=y\left(1-\left(x^2+y^2\right)\right) , y=x\left(1-\left(x_2+y^2\right)\right)
Solution : Given system of non linear equations…

How to Find Jacobian of functions given below

Question : Find Jacobian of functions given below f(x,y)=y\left(1-\left(x^2+y^2\right)\right) , g(x,y)=x\left(1-\left(x_2+y^2\right)\right)
Solution : given functions f(x,y)=y\left(1-\left(x^2+y^2\right)\right) , g(x,y)=x\left(1-\left(x_2+y^2\right)\right)
Their first order partial derivatives are \frac{\partial f}{\partial x} =…

how do you solve following system of non linear equations

Question : Solve following system of non linear equations x=y\left(1-\left(x^2+y^2\right)\right) , y=x\left(1-\left(x_2+y^2\right)\right)
Solution : x=y\left(1-\left(x^2+y^2\right)\right)
(1) y=x\left(1-\left(x_2+y^2\right)\right)
(2) From eqn (1) \frac{x}{y}=1-\left(x^2+y^2\right)
From eqn (2) \frac{y}{x}=1-\left(x^2+y^2\right)
Equating…

examples of data plot matlab

Question : Find data plot matlab for the following cases (a) x_1=\left(\begin{matrix}0\\1\\2\\3\\4\\5\\6\\7\\8\\9\\10\\\end{matrix}\right),y_1=\left(\begin{matrix}1\\0.9\\0.8\\0.7\\0.6\\0.5\\0.4\\0.3\\0.2\\0.1\\0\\\end{matrix}\right)\ \
(b) x_2=(x_i), x_i = 2i, 0\le i \le 50 , y_2 =(e^{x(i)})
Solution : (a) %program…

how do you find analytical solution of ode y’+2y=e^(-4t)+cos(2pit) such that y(0)=1

Question : Find analytical solution of ode y'+2y=e^(-4t)+cos(2pit)
such that y(0)=1 Solution : Given differential equationy^\prime+2y=e^{-4t}+\cos{\left(2\pi t\right)},y\left(0\right)=1
(1)This equation can be written in the form y^\prime+P\left(t\right)y=Q\left(t\right)
Which is Linear ODE of…