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  • Solve for genral solution. y dx plus (x minus y to the power 2) dx equals 0

Solve for general solution.

    Q11.    y dx + (x - y^2)dy = 0

Answers (1)

best_answer

Given equation is
y dx + (x - y^2)dy = 0
we can rewrite it as
\frac{dx}{dy}+\frac{x}{y}=y
This is  \frac{dx}{dy} + px = Q  type where p =\frac{1}{y} and Q =y
Now,
I.F. = e^{\int pdy}= e^{\int \frac{1}{y} dy}= e^{\log y } = y                     
Now, the solution of given differential equation is given by relation
x(I.F.) =\int (Q\times I.F.)dy +C
x(y) =\int y\times ydy +C
xy= \int y^2dy + C
xy = \frac{y^3}{3}+C
x = \frac{y^2}{3}+\frac{C}{y}
Therefore, the general solution is  x = \frac{y^2}{3}+\frac{C}{y}

Posted by

Gautam harsolia

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