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solve dy/dx=(9x+y+1)^2 by method of separable variable?

solve dy/dx=(9x+y+1)^2 by method of separable variable?
 
 
 

Grade:12th pass

2 Answers

Nandana
110 Points
5 years ago
hi ,
    first, expand (9x+y+1)^2 ,
      which is –
          d/dx(y) = 81x^2 +y^2+1+2y+81xy+81x
          take integration on both sides , then
          y = ∫ (81x2 +y2+1+2y+81xy+81x) dx
           y = 27 x3 +81/2x2y + 81/2 x2 +(y2 +1)x
         
 
          simplify further if you want
            
 
 
Nandana
110 Points
5 years ago
 
hi ,
    first, expand (9x+y+1)^2 ,
      which is –
          d/dx(y) = 81x^2 +y^2+1+2y+81xy+81x
          take integration on both sides , then
          y = ∫ (81x2 +y2+1+2y+81xy+81x) dx
           y = 27 x3 +81/2x2y + 81/2 x2 +(y2 +1)x + K
             where ‘K ‘ orbitary constant
          simplify further if you want !

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