C4 Integration Question

Find the general solution of the following diffrential equations. Leave your answer in the form y = f(x).

x^2 \frac{dy}{dx} = y + xy

\frac{dy}{dx} = y(1 + x)x^{-2}

\int (y)\ dy = \int (1 + x)x^{-2}\ dx

\frac{y^2}{2} = \int (\frac{1}{x^2} + \frac{1}{x})\ dx

\frac{y^2}{2} = \frac{-1}{x} + ln|x| + c

y = 2\sqrt{\frac{-1}{x} + ln|x| + c}

My book gives the answer as

y = Axe^{\frac{-1}{x}}

, so where have I gone (very terribly) wrong?

Thanks. :smile:

Narik

\int (y)\ dy = \int (1 + x)x^{-2}\ dx

The LHS is not correct.

Third line. :smile:

Not y, 1/y

whoops. thanks!

Narik

Find the general solution of the following diffrential equations. Leave your answer in the form y = f(x).

x^2 \frac{dy}{dx} = y + xy

\frac{dy}{dx} = y(1 + x)x^{-2}

\int (y)\ dy = \int (1 + x)x^{-2}\ dx

\frac{y^2}{2} = \int (\frac{1}{x^2} + \frac{1}{x})\ dx

\frac{y^2}{2} = \frac{-1}{x} + ln|x| + c

y = 2\sqrt{\frac{-1}{x} + ln|x| + c}

My book gives the answer as

y = Axe^{\frac{-1}{x}}

, so where have I gone (very terribly) wrong?

Thanks. :smile:

Woopsy xD 3rd line as mentioned previously.

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