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Home  >>  CBSE XII  >>  Math  >>  Model Papers

Solve the following differential equation : $(y+3x^2)\large\frac{dx}{dy}$$=x.$

1 Answer

Toolbox:
  • When the function occurs in the form of their products, we can differentiate them using product rule, which states that $uv = uv' + vu' $
Step 1:
$(y+3x^2)\large\frac{dx}{dy}$$=x$
This can be written as
$(y+3x^2)dx=xdy$
On rearranging we can write this as
$\large\frac{xdy-ydx}{x^2}$$=3$
Step 2:
On integrating we get,
$\int\large\frac{xdy-ydx}{x^2}$$=\int 3 dx$
$\large\frac{y}{x}$$=3x+c$
$y=3x^2+cx$
This is the required solution.
answered Nov 12, 2013 by sreemathi.v
 
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