Question

solve the eqution 2y"+3y'-1y=8x+2 and given the initial condition
y(0)=0, (dy/dt at t=0)=2

find y(2)

Answer #1

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Solve the di↵erential equation (t)dy/dt + 2y = 4t^2-3t + 4
subject to the initial condition y(1) = 3.

solve the given initial value problem
dx/dt=7x+y x(0)=1
dt/dt=-6x+2y y(0)=0
the solution is x(t)= and y(t)=

1. Solve the following initial value problem using Laplace
transforms.
d^2y/dt^2+ y = g(t) with y(0)=0 and dy/dt(0) = 1 where g(t) = t/2
for 0<t<6 and g(t) = 3 for t>6

Solve the differential equation (3y^2+2ty)+(2ty+t^2)dy/dt=0

y′′+3y′+2y=2e−tt with initial condition y(0)=1,y′(0)=2

Use the Laplace transform to solve the given system of
differential equations. dx/dt=x-2y dy/dt=5x-y x(0) = -1, y(0) =
6

Solve the given initial-value problem.
2y'' + 3y' −
2y = 10x2 −
4x − 15, y(0) = 0,
y'(0) = 0

Solve the following system of differential equations:
dx/dt =x+2y
dy/dt =−x+3y

Solve the initial value problem. 5d^2y/dt^2 + 5dy/dt -
y = 0; y(0)=0, y'(0)=1

1. Solve the given initial value problem. dy/dt = (t^3 +
t)/(y^2); y(0) = 2 .
2. We know from Newton’s Law of Cooling that the rate at which a
cold soda warms up is proportional to the difference between the
ambient temperature of the room and the temperature of the drink.
The differential equation corresponding to this situation is given
by y' = k(M − y) where k is a positive constant. The solution to
this equation is given...

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