Question and Answers Forum

All Questions      Topic List

Integration Questions

Previous in All Question      Next in All Question      

Previous in Integration      Next in Integration      

Question Number 139445 by aliibrahim1 last updated on 27/Apr/21

Answered by mr W last updated on 27/Apr/21

u=xy  (du/dx)=x(dy/dx)+y  (du/dx)+3u^2 =0  −(du/u^2 )=3dx  (1/u)=3x+C  (1/(xy))=3x+C  (1/(2×(1/2)))=3×2+C ⇒C=−5  (1/(xy))=3x−5  y=(1/(x(3x−5)))  y(1)=(1/(1×(3×1−5)))=−(1/2)

$${u}={xy} \\ $$$$\frac{{du}}{{dx}}={x}\frac{{dy}}{{dx}}+{y} \\ $$$$\frac{{du}}{{dx}}+\mathrm{3}{u}^{\mathrm{2}} =\mathrm{0} \\ $$$$−\frac{{du}}{{u}^{\mathrm{2}} }=\mathrm{3}{dx} \\ $$$$\frac{\mathrm{1}}{{u}}=\mathrm{3}{x}+{C} \\ $$$$\frac{\mathrm{1}}{{xy}}=\mathrm{3}{x}+{C} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}×\frac{\mathrm{1}}{\mathrm{2}}}=\mathrm{3}×\mathrm{2}+{C}\:\Rightarrow{C}=−\mathrm{5} \\ $$$$\frac{\mathrm{1}}{{xy}}=\mathrm{3}{x}−\mathrm{5} \\ $$$${y}=\frac{\mathrm{1}}{{x}\left(\mathrm{3}{x}−\mathrm{5}\right)} \\ $$$${y}\left(\mathrm{1}\right)=\frac{\mathrm{1}}{\mathrm{1}×\left(\mathrm{3}×\mathrm{1}−\mathrm{5}\right)}=−\frac{\mathrm{1}}{\mathrm{2}} \\ $$

Commented by aliibrahim1 last updated on 27/Apr/21

thx bro

$${thx}\:{bro} \\ $$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com