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Question Number 40322 by rahul 19 last updated on 19/Jul/18

$$\mathrm{Solve}:$$$$\frac{{\mathrm{d}}^2\mathrm{y}}{\mathrm{d}{x}^2}={\left(\frac{dy}{dx}\right)}^2$$

Commented by rahul 19 last updated on 19/Jul/18

$$\mathrm{Ans}:{\mathrm{C}}_2{\mathrm{e}}^{{\mathrm{C}}_{1}x}where{C}_1,{\mathrm{C}}_2=\mathrm{constant}$$

Commented by tanmay.chaudhury50@gmail.com last updated on 19/Jul/18

$$postingsomethingtoread..\mathbb{R}ealEyesrealize$$$$\mathbb{R}eallies...justforrefreshing...$$

Commented by tanmay.chaudhury50@gmail.com last updated on 19/Jul/18

Commented by rahul 19 last updated on 19/Jul/18

oh! ������������

Answered by tanmay.chaudhury50@gmail.com last updated on 19/Jul/18

$$p=\frac{dy}{dx}$$$$\frac{dp}{dx}=p^{2}so\int p^{-2}dp=\int dx$$$$-\frac{1}{p}=x+c_1$$$$-\frac{dx}{dy}=x+c_1$$$$\frac{dx}{x+c_1}=-dyhenceln(x+c_1)=-y+{lnc}_2$$$$-y=ln\left(\frac{x+c_1}{c_2}\right)y=ln\left(\frac{c_2}{x+c_1}\right)$$

Commented by rahul 19 last updated on 19/Jul/18

$$\mathrm{Ans}.\mathrm{given}\mathrm{in}\mathrm{book}\mathrm{is}\mathrm{not}\mathrm{correct},\mathrm{right}?$$

Commented by tanmay.chaudhury50@gmail.com last updated on 19/Jul/18

$$ansmaybeinmanyformat...tocheckpls$$$$differentiate..$$

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