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3 years ago

Which of the following is a solution to the differential equation xy′−3y=6 ?

Mathematics

1 answer:

ololo11 [35]3 years ago

4 0

Answer:

$y = 5 {x}^{3} - 2$

Step-by-step explanation:

The given differential equation is :

xy′−3y=6

We want to determine which of the following options is a solution to the differential equations.

The function that satisfies the differential equation is a solution.

We can verify that

$y = 5 {x}^{3} - 2$

satisfy this differential equation.

We differentiate to get:

$y' = 15 {x}^{2}$

We substitute the function and its derivative into the differential equation to get:

$x(15 {x}^{2}) - 3(5 {x}^{3} - 2) = 6$

We expand and simplify on the left:

$15 {x}^{3}- 15 {x}^{3} + 6= 6$

This simplifies to:

$6 = 6$

Verified.

We can show that all the other functions do not satisfy this differential equation

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2 years ago

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lukranit [14]

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A²+B²=C²
We have bits of information that'll help us simplify the equation so there's only one variable.
The longer leg, A, is 3 inches more than the length of the shorter leg, B, tripled.
A=3B+3
Let's plug that in.
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The hypotenuse, C, is 3 inches less than four times the length of the shorter leg. C=4B-3
Let's plug that in.
(3b+3)²+B²=(4B-3)²
Let's solve.
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10B²+18B+9=16b²-24b+9
Let's subtract 9 from both sides.
10b²+18b=16b²-24b
Let's subtract 10b² from both sides.
18b=6b²-24b
Let's add 24b from both sides.
42b=6b²
Let's divide each side by 6.
7b=b²
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Now, let's look back at the bits of information.
The longer leg of a right triangle is 3 inches more than the length of the shorter side tripled.
3(7)+3=24
So, the longer side is 24. We can either use the other information or plug it into the equation. We can do both.
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4(7)-3=25
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Hello!

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