Question

find the solution of this equation​

Answer 1

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 :)