find the solution of this equation
Answers
Answer:
1. Simplify
d^4y/ dx4
2. d^4 divided by d^1 = d^(4 - 1) = d^3
3. d^3 y/x^4+ y = 0
4. Adding a whole to a fraction
Rewrite the whole as a fraction using x4 as the denominator :
y =y/1=y×x^4/x^4
Equivalent fraction : The fraction thus generated looks different but has the same value as the whole
Common denominator : The equivalent fraction and the other fraction involved in the calculation share the same denominator.
5. Adding up the two equivalent fractions
Add the two equivalent fractions which now have a common denominator
Combine the numerators together, put the sum or difference over the common denominator then reduce to lowest terms if possible:
d^3 y + y × x^4/x^4= d^3 y + yx^4 /x^4
6. Pull out like factors :
d3y + yx4 = y × (d3 + x4)
7. y × (d^3 + x^4)/x^4 = 0 -----3rd step
8. When a fraction equals zero ...
Where a fraction equals zero, its numerator, the part which is above the fraction line, must equal zero.
Now,to get rid of the denominator, Tiger multiplys both sides of the equation by the denominator.
Here's how:
y×(d^3+x^4) / x^4 × x^4 = 0
Now, on the left hand side, the x4 cancels out the denominator, while, on the right hand side, zero times anything is still zero.
The equation now takes the shape :
y × (d3+x4) = 0
9. A product of several terms equals zero.
When a product of two or more terms equals zero, then at least one of the terms must be zero.
We shall now solve each term = 0 separately
In other words, we are going to solve as many equations as there are terms in the product
Any solution of term = 0 solves product = 0 as well.
10. Solve : y = 0
Solution is y = 0
11. x=0
y=0
Hope it helps :)