consider the differential equation
x^2 (dy/dx)= x^3+3(x^2)y+x(y^2)......................…
make the substitution u=y/x
to reduce it to
x(du/dx) = 1+2u+u^2................................…
solve equation 2 for u(x) and hence write down the solution y(x) for equation 1
The answer is
y= -x - [x / (logx + c)]
I got no idea how that is can someone please show the working out
Thankyou so so much
x^2 (dy/dx)= x^3+3(x^2)y+x(y^2)......................…
make the substitution u=y/x
to reduce it to
x(du/dx) = 1+2u+u^2................................…
solve equation 2 for u(x) and hence write down the solution y(x) for equation 1
The answer is
y= -x - [x / (logx + c)]
I got no idea how that is can someone please show the working out
Thankyou so so much
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I'm almost positive you made a mistake copying this. The substitution doesn't work at all,and the solution to the DE you have there is this ridiculous mess that no one should ever see. However, if that IS the correct DE, then disregard it, because it's nigh unsolvable.
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Huang lee