7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt 7. Solve the following differential equations. dy 2 y= 5x, x>0. + a) dx dx 1+2x 4e', t>0 b) t dt
Question 2. (15 pts) Solve the IVP. dy/dt t/(y+ty), y(1) 2 Question 2. (15 pts) Solve the IVP. dy/dt t/(y+ty), y(1) 2
Solve the given initial value problem. x(0) = 1 dx = 4x +y- e 3t, dt dy = 2x + 3y; dt y(0) = -3 The solution is X(t) = and y(t) =
a) Solve the IVP: (x + y)2dx + (2xy + x2 - 1)dy = 0 ; y(1) = 1 b) Find a continuous solution satisfying the given De subject to initial condition. dy + 2x y = f(x), f(x) = fx, 05x<1 y(0) = 2 dx 10, 821 c) Solve the Bernoulli's equation xy' + y = x²y2
Solve the given initial value problem. = 4x + y - e (0) = 2 dt dy dt =x+uya (0) = -3 The solution is x(t)= and y(t)=
Solve the system of differential equations dx/dt = x-y, dy/dt = 2x+y subject to the initial conditions x(0)= 0 and y(0) = 1.
Solve for y(t). dy/dt + 2x = et dx/dt-2y= 1 +t when x(0) = 1, y(0) = 2
2. Solve the ODE/IVP: 4x²y" +8xy' +y=0; y(1)= 2, y'(1) = 0).
Find dy/dt using the given values. y = x - 4x for x = 3, dx/dt = 2. y = [ X dt . dx/dt = 2. Enter an exact number
Solve the following IVP: dy/dx + 4y - e^-x = 0 ; y(0) = 4/3