Solving simple differential equations involve the process of differentiating the algebraic function with respect to the input function. The algebraic function which is differentiable is known as differential equations. The differential equation comes under calculus category whereas to find the rate of change of the given function with respect to the input function. The following are simple example differential equations for solving.
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Simple Differential Equations Examples for Solving:
The following are the example problems with simple differential equations for solving.
Example 1:
Solve the simple differential equation.
f(k) = k2 – 4k + 8
Solution:
The given equation is
f(k) = k 2 – 4k + 8
The first derivative f ' for the algebraic function is
f '(k) = 2 k – 4
Example 2:
Solve the simple differential equation.
f(k) = k 3 – 5 k 2 + 11k
Solution:
The given function is
f(k) = k 3 – 5 k 2 + 11k
The first derivative f ' for the algebraic function is
f '(k) = 3k 2 – 5(2 k ) + 11
f '(k) = 3k 2 – 10 k + 11
Example 3:
Solve the simple differential equation.
f(k) = k4 – 3k 3 – 4k 2 + k
Solution:
The given function is
f(k) = k4 – 3k 3 – 4 k 2 + k
The first derivative f ' for the algebraic function is
f '(k) = 4 k 3 – 3(3k 2 ) – 4( 2 k ) + 1
f '(k) = 4 k 3 – 9k 2 – 8 k + 1
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Example 4:
Solve the simple differential equation.
f(k) = k 5 – 6 k 3 + 11
Solution:
The given function is
f(k) = k 5 – 6 k 3 + 10
The first derivative f ' for the algebraic function is
f '(k) = 5k 4 – 6(3 k 2 )
f '(k) = 5k 4 – 18 k 2
Simple Differential Practice Equations for Solving:
1) Solve the simple differential equation.
f(k) = k 3 – 6 k 2 + 11k
Answer: f '(k) = 3k 2 – 12 k
2) Solve the simple differential equation.
f(k) = k 2 – 6 k + 11
Answer: f '(k) = 2k – 6
