CUET Preparation Today
The solution $x^2\frac{dy}{dx}=x^2+xy+y^2$ is: |
$\tan^{-1}\frac{y}{x}=\log y + c$ $\tan^{-1}\frac{x}{y}=\log x + c$ $\tan^{-1}\frac{x}{y}=\log y + c$ $\tan^{-1}\frac{y}{x}=\log x + c$ |
$\tan^{-1}\frac{y}{x}=\log x + c$ |
$\frac{dy}{dx}=1+\frac{y}{x}+(\frac{y}{x})^2$ Substitute $\frac{y}{x}=t⇒\frac{dy}{dx}=t+x\frac{dt}{dx}$ $⇒x.\frac{dt}{dx}=1+t^2⇒\int\frac{dt}{1+t^2}=\int\frac{dx}{x}$ $⇒\tan^{-1}t=ln\,x+c⇒\tan^{-1}\frac{y}{x}=ln\,x+c$ |
