# Differential Equations

## Question

1) A force of 400 newtons stretches a spring 4 m. A mass of 50 kg is attached to the end of the spring and released from the equilibrium position with an upward velocity of 10 m/sec. Find the equation of motion.

2) Solve the DE subject to the given initial conditions.
x^2y" - 3xy' + 4y = 0, y(1) = 5, y'(1) = 3

3) Find the solution to the DE using power series
(x^2 + 1)y" + xy' - y = 0

## Solution Preview

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1) 50x'' + 100x = 0; x(0) = 0; x'(0) = -10

50u^2 + 100 = 0

u^2 = -2

u = +/- sqrt(2) i

x = c1 sin(sqrt(2) t) + c2 cos(sqrt(2) t)

x(0)=0 requires c2 = 0

x'(0) = -10 requires -10 = sqrt(2) c1...
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