Practicing Success
Practicing Success
CUET Preparation Today
General solution of the differential equation $\frac{2y\, dx-3x\, dy}{y}=0$ is (c is an arbitrary constant) |
$y=cx$ $y^3=x^2$ $y^3=cx^2$ $y=cx^2$ |
$y^3=cx^2$ |
$\frac{2ydx}{y}-\frac{3xdy}{y}=0⇒\frac{2ydx}{y}=\frac{3xdy}{y}$ $⇒\int\frac{2}{x}dx=\int\frac{3}{y}dy$ (integrating both sides) $⇒2\log x=3\log y+\log c$ $⇒\log x^2=\log y^3c$ so $y^3c=x^2$ so $y^3=cx^2$ |
