2. Solve the initial value problem for the given differential equation. 2. Solve the initial value problem for the given differential equation.
Differential Equation Please answer both of the questions below Thanks! Solve the given initial value problem. y'' + 36y = 0; y(0) = 3, y'(O) = 5 x(t) = Find a general solution to the differential equation using the method of variation of parameters. y'' + 2y' +y=2e -t The general solution is y(t) = .
(b) [6 points) Transform the given initial value problem for the single differential equation of second order into an initial value problem for two first order equations. (Do not attempt to solve it!) u" + -u' +4u= 2 cos(3t), u(0) = 1, u'(0) = -2.
Solve the given differential equation by separation of variables. dP/dt= P-P2 Solve the given differential equation by separation of variables. dN/dt + N = Ntet+3 Solve the given differential equation by separation of variables. Find an explicit solution of the given initial-value problem.
Solve the following initial value problem for r as a function of t. Differential equation: Initial conditions: dar -= 3e ti -2e - tj + 9e 3tk dt? r(0) = 71 + 2 + 4k dr = - +5j dt 0
No 4. Solve the differential equation dy dx . Solve the initial value problem: y" + 3y' + 2y 10 cosx, y(0) 1,y'(0) 0
Solve the initial value problem for r as a vector function of t. dr Differential equation: = -32k . = 21 + 2] Initial conditions: r(0) = 60k and r(t) = (i+1+OK
Solve the initial value problem for r as a vector function of t. dr Differential equation: of = -7t i-5t j - 3t k Initial condition: r(0) = 7i + 2+ 3k r(t) = (O i+();+ ( Ok
exact differential equations 2. Solve the initial value problem: (2.1 – y) + (2y – r)y' = 0) with y(1) = 3. 3. Find the numerical value of b that makes the following differential equation exact. Then solve the differential equation using that value of b. (xy? + br’y) + (x + y)x+y = 0
Solve the following differential equation with given initial condition. y' = 11ty - 16t, y(0) = 4 Write the integral equation that results from applying the separation of variables technique. Write the particular solution that solves the initial value problem.
differential equations Use the Laplace transform to solve the given initial-value problem. y' + 3y = et, y(0) = 2 y(t) =