Solve the differential equation
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A tightly stretched string with fixed end points x = 0 and x = l is initially in a position
given by y = y0sin3 . It is released from rest from the initial position. Find the displacement y(x,t).
If being positive constants) and x = a′ and
when t = 0, show that
Using the method of undetermined coefficients, find the general solution of the DE yiv - 2ym + 2yn. = 3e-x + 2e-x x + e-x sinx.
Find a continuous solution of the IVP
where g(t) = .
Find the complete integral of the equation z2 x1 x2 x3.
Classify the following as true or false giving reasons for your answers..
i). For the IVP, = f(x,y), y(x0) = y0 , the continuity of f(x,y) and
guarantees the unique solution of the problem.
ii). Equations
and
have the same normal form.
iii). Equation cos(x + y) p + sin(x + y)q = z2 + z is a quasi-linear equation.
iv).
is a non -linear PDE.
v). Every solution of the ordinary differential equation (D2 + 1)2 y = 0 is bounded on [0, ∞] .
Find the differential equation of the family of curves x2 + y2 + 2ax + 2by + c = 0 , where a,b,c, are parameters.