The unique solution y(x) of an ordinary differential equation:
exists
The unique solution \( y(x) \) of the given ordinary differential equation exists for all \( x \in \mathbb{R} \).
The equation describes a piecewise function:
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The differential equation:
is a second order differential equation of degree 3.
Show that the limit of the function exists at the origin, where:
Do the repeated limits of exist? Justify your answer.
The rate of change of the price of a commodity is proportional to the difference between the demand D and the supply S. If
and
where a, and
are constants, determine
It is given that at
f) Differential equation:
in is a linear, homogeneous equation.
If cos and α,cosβ cos γ are the direction cosines of a line, then show that:
A real-valued function of three variables which is continuous everywhere is differentiable.
Solve the differential equation: