PHYSICS 312

PROBLEM SET 1:
Given Jan. 6. Due Jan.15. 1999.


1:Solve

$$\frac{du}{dt}+tu=t$$

with u(0)=1.

2: The differential equation

$$t^2\frac{d^2u}{dt^2}+\frac{1}{4}u=0$$

has

$$u=\sqrt{t}$$

as a solution. Find a second linearly independent solution.


3: Find the general solution to

$$\frac{d^4u}{dx^4}-2a^2\frac{d^2u}{dx^2}+a^4u=0$$

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