Differential Equations

Methods of Solving First order, First Degree Differential Equations

  • Variable separable method is used to solve such an equation in which variables can be separated completely i.e. terms containing y should remain with dy and tems containing x should remain with dx.

Part1: View the Topic in this video From 00:12 To 13:26

Part2: View the Topic in this video From 00:10 To 08:40

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1. xdy + ydx = d (xy)

2. d(x + y) = dx + dy

3. d\left(\frac{y}{x}\right)=\frac{xdy-ydx}{x^2}

4. d\left(\frac{x}{y}\right)=\frac{ydx-xdy}{y^2}

5. d\left(\frac{x^2}{y}\right)=\frac{2xydx-x^{2}dy}{y^2}

6. d\left(\frac{y^2}{x}\right)=\frac{2xydy-y^{2}dx}{x^2}

7. d\left(\frac{x^2}{y^{2}}\right)=\frac{2xy^{2}dx-2x^{2}ydy}{y^4}

8. d\left(\frac{y^2}{x^{2}}\right)=\frac{2x^{2}ydy-2xy^{2}dx}{x^4}

9. \frac{xdy+ydx}{xy}=d(\log xy)

10. \frac{ydx-xdy}{xy}=d\left(\log \frac{x}{y}\right)

11. \frac{xdy-ydx}{xy}=d\left(\log \frac{y}{x}\right)

12. \frac{dx+dy}{x+y}=d \log (x+y)

13. \frac{xdx+ydy}{x^{2}+y^{2}}=d \left(\log \sqrt{x^{2}+y^{2}}\right)

14. \frac{xdy-ydx}{x^{2}+y^{2}}=d \left(\tan^{-1}\frac{y}{x}\right)

15. \frac{ydx-xdy}{x^{2}+y^{2}}=d \left(\tan^{-1}\frac{x}{y}\right)

16. d \left(\frac{-1}{xy}\right)=\frac{xdy+ydx}{x^{2}y^{2}}

17. d \left(\frac{e^{x}}{y}\right)=\frac{ye^{x}dy-e^{x}dy}{y^{2}}

18. d \left(\frac{e^{y}}{x}\right)=\frac{xe^{y}dy-e^{y}dx}{x^{2}}