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andre [41]
3 years ago
6

Solve the differential equation x^3y"'− 3x^2 y" 6xy'−6y = 0.

Mathematics
1 answer:
Anna [14]3 years ago
3 0
<span>Equation at the end of step  1  :</span><span> (((x3)•y)-(((3x2•y6)•x)•y))-6y = 0 </span><span>Step  2  :</span><span>Step  3  :</span>Pulling out like terms :

<span> 3.1 </span>    Pull out like factors :

  <span> -3x3y7 + x3y - 6y</span>  =  <span> -y • (3x3y6 - x3 + 6)</span> 

Trying to factor a multi variable polynomial :

<span> 3.2 </span>   Factoring   <span> 3x3y6 - x3 + 6</span> 

Try to factor this multi-variable trinomial using trial and error<span> 

 </span>Factorization fails

<span>Equation at the end of step  3  :</span><span> -y • (3x3y6 - x3 + 6) = 0 </span><span>Step  4  :</span>Theory - Roots of a product :

<span> 4.1 </span>   A product of several terms equals zero.<span> 

 </span>When a product of two or more terms equals zero, then at least one of the terms must be zero.<span> 

 </span>We shall now solve each term = 0 separately<span> 

 </span>In other words, we are going to solve as many equations as there are terms in the product<span> 

 </span>Any solution of term = 0 solves product = 0 as well.

Solving a Single Variable Equation :

<span> 4.2 </span>     Solve  :    -y = 0<span> 

 </span>Multiply both sides of the equation by (-1) :  y = 0 

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