Question and Answers Forum

All Questions      Topic List

Algebra Questions

Previous in All Question      Next in All Question      

Previous in Algebra      Next in Algebra      

Question Number 97818 by I want to learn more last updated on 09/Jun/20

$$\mathbf{if}{\mathbf{y}}^2={\mathbf{ax}}^2+\mathbf{bx}+\mathbf{c}$$$$\mathbf{Show}\mathbf{that}:\mathbf{y}\frac{{\mathbf{d}}^3\mathbf{y}}{{\mathbf{dx}}^3}+3\frac{\mathbf{dy}}{\mathbf{dx}}\frac{{\mathbf{d}}^2\mathbf{y}}{{\mathbf{dx}}^2}=0$$

Answered by Rio Michael last updated on 09/Jun/20

$$y^2={ax}^2+bx+c$$$$\Rightarrow 2y\frac{dy}{dx}=2ax+b$$$$\Rightarrow 2y\frac{d^{2}y}{{dx}^2}+2{\left(\frac{dy}{dx}\right)}^2=2a$$$$2y\frac{d^{3}y}{{dx}^3}+2\frac{dy}{dx}.\frac{d^{2}y}{{dx}^2}+4\frac{d^{2}y}{{dx}^2}\frac{dy}{dx}=0$$$$\Rightarrow 2y\frac{d^{3}y}{{dx}^3}+6\frac{dy}{dx}\frac{d^{2}y}{{dx}^2}=0$$$$\Rightarrow y\frac{d^{3}y}{{dx}^3}+3\frac{dy}{dx}\frac{d^{2}y}{{dx}^2}=0\mathrm{proved}!$$

Commented by I want to learn more last updated on 09/Jun/20

$$\mathrm{Thanks}\mathrm{sir}$$

Terms of Service

Privacy Policy

Contact: info@tinkutara.com