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Question : Find analytical solution of ode \[y'+2y=e^(-4t)+cos(2pit)\] such that y(0)=1 Solution : Given differential equation\[y^\prime+2y=e^{-4t}+\cos{\left(2\pi t\right)},y\left(0\right)=1\] (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…

Question : Plot slope field matlab of the following ode \[\frac{dx}{dt} = t^2-x^2\] Solution : % Matlab program to Plot slope field matlab of the following ode [t,x] = meshgrid(-5:0.2:5,-5:0.2:5);…

Question : Plot direction field matlab of the following ode \[\frac{dx}{dt} =1+x-2xt\] Solution : %plot direction field matlab program of the ode [t,x] = meshgrid(-5:0.2:5,-5:0.2:5); n = size(t); u =…

Question : Find numerical solution of the following ode using Euler method matlab \[\frac{dx}{dt} = 1-2x-xt , x(0) =0\] with h = 0.2 and plot the solution in the interval…

Question : Find analytical solution of the following ode in matlab \[\frac{dx}{dt} = 1+t-2x, x(0) =0\] Solution : %matlab program to find analytical solution of the ode dx/dt =1+t-2x subject…

Question : Find equation of circle with (a) radius 1 and center (1, 1) (b) radius 1 and center (1, -1) Solution (a) : We know that Equation of circle…

Question : Find equations of circles which touches three lines x=0, y=0 and x= c. Solution : Suppose c>0 There are two circles which touches three lines y=0 and x=…

Question : The equation of circles which touches x=0, y=0, and x =c is Solution : Suppose c>0 Radius of the circles which touches \[x=0, y=0, and x =c is…

Question : The line joining the points (1,3) and (2,7) is divided by the line 3 x+ y = 9 in the ratio Solution : The points (1,3) and (2,7)…

Question : Find the equation of line joining two points (1,3) and (2,7). Solution : Equation of line joining two points \[(x_1\ ,y_1),\ (x_2,\ y_2)\] is given as \[y-y_1=\frac{y_2-y_1}{x_2-x_1}\left(x-x_1\right) (1)\]…