Find the slope of the line that passes through (6, 4) and (4, 5).
2 answers:
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Answer:
Step-by-step explanation:
(A) The difference between an ordinary differential equation and an initial value problem is that an initial value problem is a differential equation which has condition(s) for optimization, such as a given value of the function at some point in the domain.
(B) The difference between a particular solution and a general solution to an equation is that a particular solution is any specific figure that can satisfy the equation while a general solution is a statement that comprises all particular solutions of the equation.
(C) Example of a second order linear ODE:
M(t)Y"(t) + N(t)Y'(t) + O(t)Y(t) = K(t)
The equation will be homogeneous if K(t)=0 and heterogeneous if
Example of a second order nonlinear ODE:
(D) Example of a nonlinear fourth order ODE:
For the ODE
multiply both sides by <em>t</em> so that the left side can be condensed into the derivative of a product:
Integrate both sides with respect to <em>t</em> :
Divide both sides by to solve for <em>y</em> :
Now use the initial condition to solve for <em>C</em> :
So the particular solution to the IVP is
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