FT DE 3-3 [1] Solve for the GS of (D4-5D³+9D²-7D+2)y=0 [2] Determine the roots of the auxiliary equation y=x²-e2*cosx for a homogeneous linear equation with real, constant coefficients. [3] Solve for the GS of (D²-5D+6)y=cosx+2x

The given equation is in a form of A(x) + B(x)y = C(x). dx O variable separable equation O Non-exact equation exact equation O linear equation of order one

conyert the differential equation a system and solve the system: (B t 4D+ 5)y = 0 HOD CIVIL DEPT.

X=4/5y Y=3x+7 Solve using substitution. (X,y)= ( )

Change of variables in a Bernoulli equation The equation y'(t) + ay = by", where a, b, and p are real numbers, is called a Bernoulli equation. Unless p = 1, the equation is nonlinear and would appear to be difficult to solve-except for a small miracle. Through the change of variables v(t) = (y(t))'-P, the equation can be made linear. Carry out the following steps. a. Letting v = y!-P, show that y'(t) = y(1)P -v'(t). b. Substitute this expression for y' (t) into the differential equation and simplify to obtain the new (linear) equation v'(t) = a(1 – p)v = b(1 – p), which can be solved using the methods of this section. The solution y of the original equa- tion can then be found from v.

LINEAR DE

A linear second-order non-homogeneous equation models this scenario: People falling at a height of 100ft above the ground attached to a 100-foot rope into a pit that's cut off at 75 feet underground. Spring constant of the rope is 120 lbs/ft, and air resistance is 5 times the instantaneous velocity. M is mass of person and g is gravity. Note that the pit is actually 100 ft deep, it's just cut off 25 ft from the bottom to make the pit 75 feet deep. What are the initial conditions of the height y(t) of the person falling at time t? The equation is my''+5y'+120y=mg

Linear Equation with Constant Coefficient

dP/dt = P - P2 ; solve by seperation of variables.