Your first differential equation is incomplete, so I'll just look at the second one.
<em>y'</em> + 2<em>xy</em> = 4<em>x</em>
Multiply both sides by exp(<em>x</em> ²):
exp(<em>x</em> ²) <em>y'</em> + 2<em>x</em> exp(<em>x</em> ²) <em>y</em> = 4<em>x</em> exp(<em>x</em> ²)
The left side is the derivative of a product:
(exp(<em>x</em> ²) <em>y</em> )<em>'</em> = 4<em>x</em> exp(<em>x</em> ²)
Integrate both sides:
exp(<em>x</em> ²) <em>y</em> = ∫ 4<em>x</em> exp(<em>x</em> ²) d<em>x</em>
For the integral, substitute <em>u</em> = <em>x</em> ² and d<em>u</em> = 2<em>x</em> d<em>x</em> :
exp(<em>x</em> ²) <em>y</em> = 2 ∫ exp(<em>u</em>) d<em>u</em>
Solve for <em>y</em> :
exp(<em>x</em> ²) <em>y</em> = 2 exp(<em>u</em>) + <em>C</em>
exp(<em>x</em> ²) <em>y</em> = 2 exp(<em>x</em> ²) + <em>C</em>
<em>y</em> = 2 + <em>C</em> exp(-<em>x</em> ²)
Answer:
44499869368695576 (4.44998693 x 10 to the 16th power) < Decimal version
Step-by-step explanation:
Step-by-step explanation:
Distance between two villages = d
Answer:
Please find attached the graph of the given data created with Microsoft Excel
Step-by-step explanation:
The question is a word problem with which we construct a table of values and then graph the data as follows;
The graph of the above data in created using the Chart options in the Insert menu of Microsoft Excel as seen in the attached image
Answer:
There is a whole range of speeds at which you are allowed to drive, not just one. In cases like this where there is more than one correct answer, we use inequalities, not equations, to represent the situation.
Inequalities are mathematical statements that define a range of values. They are easily recognizable because they contain the symbols <, ≤,>, or ≥.
