The first solution is quadratic, so its derivative y' on the left side is linear. But the right side would be a polynomial of degree greater than 1, so this is not the correct choice.
The third solution has a similar issue. The derivative of √(x² + 1) will be another expression involving √(x² + 1) on the left side, yet on the right we have y² = x² + 1, so that the entire right side is a polynomial. But polynomials are free of rational powers, so this solution can't work.
This leaves us with the second choice. Recall that
1 + tan²(x) = sec²(x)
and the derivative of tangent,
(tan(x))' = sec²(x)
Also notice that the ODE contains 1 + y². Now, if y = tan(x³/3 + 2), then
y' = sec²(x³/3 + 2) • x²
and substituting y and y' into the ODE gives
sec²(x³/3 + 2) • x² = x² (1 + tan²(x³/3 + 2))
x² sec²(x³/3 + 2) = x² sec²(x³/3 + 2)
which is an identity.
So the solution is y = tan(x³/3 + 2).
Answer: you need to dived and then you will get your answer
Step-by-step explanation:
Answer:
D) -2
Step-by-step explanation:
Answer:
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x=3
y=-5
z=-4
Answer:
The value of the z is 12 .
Step-by-step explanation:
Definition of vertically opposite angle .
Vertically opposite angles is defines angles opposite to each other when two lines cross eachother .
Thus
(5z + 8)° = (4z + 20)°
(5z + 8) = (4z + 20)
Open the bracket
5z + 8 = 4z + 20
5z - 4z = 20 -8
z = 12
Therefore the value of the z is 12 .
