Originally Posted by

**Hellbent** Hi,

Help needed. How is (a) done?

(a) The variables x and y are related by the differential equation $\displaystyle \frac{dy}{dx}\,+\,\frac{y}{x}\,=\,y^3$$\displaystyle

$

(i) State clearly why the integrating factor method cannot be used to solve this equation. Mr F says: What is the general form of DE for which the integrating factor method can be used ...? Compare this to what you have.

(ii) The variables y and z are related by the equation $\displaystyle \frac{1}{y^2}\,=\,-2z$. Show that $\displaystyle \frac{dz}{dx}\,-\,\frac{2z}{x}\,=\,1$. Mr F says: Substitute -2z = 1/y^2 into the given DE.

(iii) Find the solution of the differential equation $\displaystyle \frac{dy}{dx}\,+\,\frac{y}{x}\,=\,y^3,\,$ given that $\displaystyle y\,=\,2\,\,when\,\,x\,=\,1$. Mr F says: Solve the DE in part (ii) and then back-substitute -2z = 1/y^2.

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