CUET Preparation Today
I.F. for y ln y $\frac{dx}{dy}$ + x − ln y = 0 is : |
ln x ln y ln xy none of these |
ln y |
The correct answer is Option (2) → $ln\, y$ $y\, ln\, y\frac{dx}{dy} + x - ln\, y = 0$ $⇒y\, ln\, y\frac{dx}{dy} + x=ln\, y$ $⇒\frac{dx}{dy}+\frac{1}{y\, ln\, y}+x=\frac{1}{y}$ $I.F.=e^{\int P\,dy}$ $=e^{\int \frac{1}{y\, ln\, y}dy}$ $=e^{ln|ln\,y|}=ln\,y$ |
