A) Solve the initial value problem:
8x−4y√(x^2+1) * dy/dx=0
y(0)=−8
y(x)=
B) Find the function y=y(x) (for x>0 ) which
satisfies the separable differential equation
dy/dx=(10+16x)/xy^2 ; x>0
with the initial condition y(1)=2
y=
C) Find the solution to the differential equation
dy/dt=0.2(y−150)
if y=30 when t=0
y=
Consider the equation uux + uy = 0 with the initial
condition
u(x, 0) = h(x) = ⇢ 0 for x > 0
uo for x < 0, with
uo< 0.
Show that there is a second weak solution with a shock along the
line x = uo y / 2
The solution in both mathematical and graphical presentation
before and after the shock.