University of Rhode Island
Practice problems for
1. Solve the following initial
value problem for the differential equation:
2. Find the general
solution of the homogeneous differential equation: dy/dx = y ( y2
+ 3 x2 )
/ ( 2 x3 ).
sin(x) y = 1
|y(0) = 1.
3. Find the general solution of the
exact differential equation: (2x - y sin (x) +
2 e2x+y )dx + ( cos x + e2x+y )dy=0 .
the following initial value problem for the Bernoulli differential
|y' - x
y = x y2
|y(0) = -2.
the following initial value problem:
+ 5 x y' + 29 y = 0
|y(1) = -2, y'(1)
Use the method of reduction of order or Abel's formula to find a second
linearly independent solution of the following differential equation
with the given solution:
Find the particular solution of this equation that satisfies the
initial condition y(1) =1, y'(1) =
- 1) y'' - x y'
+ y = 0
Can you justify the
uniqueness of the solution of this IVP without finding the general
solution of the above equation ? Explain.