Question Number 30187 by abdo imad last updated on 17/Feb/18
$${solve}\:{xy}^{'} \:−\mathrm{2}{y}\:=\:{x}^{\mathrm{4}} \:. \\ $$
Answered by ajfour last updated on 18/Feb/18
$$\frac{{dy}}{{dx}}−\left(\frac{\mathrm{2}}{{x}}\right){y}={x}^{\mathrm{3}} \\ $$$${e}^{−\int\frac{\mathrm{2}}{{x}}{dx}} \:=\:{e}^{−\mathrm{2ln}\:{x}} \:=\:\frac{\mathrm{1}}{{x}^{\mathrm{2}} } \\ $$$$\:\Rightarrow\:\:\frac{{y}}{{x}^{\mathrm{2}} }\:=\:\int{xdx}\:+{c}_{\mathrm{1}} \\ $$$${or}\:\:\:\:\frac{{y}}{{x}^{\mathrm{2}} }\:=\:\frac{{x}^{\mathrm{2}} }{\mathrm{2}}\:+{c} \\ $$$${or}\:\:\:\:\:\:\:\:\:\:\boldsymbol{{y}}\:=\:\frac{\boldsymbol{{x}}^{\mathrm{4}} }{\mathrm{2}}+\boldsymbol{{cx}}^{\mathrm{2}} \:\:\:. \\ $$