Question and Answers Forum

All Questions      Topic List

Differential Equation Questions

Previous in All Question      Next in All Question      

Previous in Differential Equation      Next in Differential Equation      

Question Number 1603 by 123456 last updated on 25/Aug/15

$$\frac{f\left(x\right)}{f^{\prime }\left(x\right)}=\frac{f^{\prime }\left(x\right)}{f\left(x\right)}$$$$f\left(x\right)=$$

Answered by Rasheed Soomro last updated on 28/Aug/15

$${\left[f{}^{\prime }\left(x\right)\right]}^2={\left[f\left(x\right)\right]}^2$$$$f{}^{\prime }\left(x\right)=\pm f\left(x\right)$$$$Letf\left(x\right)=y$$$$\frac{dy}{dx}=\pm y\Rightarrow \left(\frac{1}{y}\right)\frac{dy}{dx}=\pm 1$$$$\Rightarrow \int \left[\left(\frac{1}{y}\right)\frac{dy}{dx}\right]dx=\int (\pm 1)dx$$$$ln\mid y\mid +c=\pm x+c$$$$ln\mid y\mid =\pm x+c$$$$y=e^{\pm x+c}=e^{\pm x}.e^c={ke}^{\pm x}$$$$f\left(x\right)={ke}^{\pm x}$$

Commented by 123456 last updated on 27/Aug/15

$$y=e^{\pm x+c}=e^{\pm x}{e}^c={ke}^{\pm x}$$

Commented by Rasheed Soomro last updated on 27/Aug/15

$$\mathbf{Thanks}\mathbf{for}\mathbf{mentioning}\mathbf{and}\mathbf{correcting}\mathbf{my}\mathbf{mistake}.$$$$\mathbf{Pl}\mathbf{continue}\mathbf{same}\mathbf{practice}\mathbf{as}\mathbf{I}\mathbf{want}\mathbf{to}\mathbf{learn}.$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com