Find the general solution of this ODE: d'y dt² The solution will be of the form: dy +10. +24y= 4t² + 7t + 1 dt y(t) = Cy₁(t) + Dy2(t) + Yp(t) so use C and D as the arbitrary constants. y(t):

Q: Determine whether it is stable or unstable. D) dx₁ dt = 3x₁x2-x1 + x2 dx₂ dt =x²-x₁

A: D Given system of differential equation is dx1dt=3x1x2−x1+x2dx2dt=x22−x1 We have to determine…

Q: find dy/dt.

A:

Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: Consider the two ODEs dy dx dy dx +y=0 + y² = 0 equil eq.2 (a) How are the two equations different…

A:

Q: dx h-16x²

A: NOTE: Refresh your page if you can't see any equations. . ..................(1) substitute…

Q: Find f, (9,0) if f(x,y) = 4x eY. fy(9,0) = (Simplify your answer.) %3D

A: We can find the required answer as below

Q: 9. y(y² + 1)dx + x(y²-1)dy = 0 Ans: + xy = c

A: We  are given the differential equation to be solved    =>       y(y² + 1)dx + x(y²-1)dy = 0

Q: solve this D.E using separation of variables dy/dx = (xy+3x-y-3)/(xy -2x+4y-8)

A:

Q: 4-3x Consider the function y=e¹-3. Find y'.

A:

Q: d³r dz +t- dt3 (c) 4tx = 0 %3D dt

A: The solution is given as