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dy-dx-1-y-2-x-solve-the-differential-equation-




Question Number 9461 by tawakalitu last updated on 09/Dec/16
(dy/dx) = ((1 + y)/(2 + x))  solve the differential equation.
$$\frac{\mathrm{dy}}{\mathrm{dx}}\:=\:\frac{\mathrm{1}\:+\:\mathrm{y}}{\mathrm{2}\:+\:\mathrm{x}} \\ $$$$\mathrm{solve}\:\mathrm{the}\:\mathrm{differential}\:\mathrm{equation}. \\ $$
Answered by mrW last updated on 09/Dec/16
(dy/(1+y))=(dx/(2+x))  ∫(dy/(1+y))=∫(dx/(2+x))  ∫((d(1+y))/(1+y))=∫((d(2+x))/(2+x))  ln (1+y)=ln (2+x)+ln c=ln c(2+x)  1+y=c(2+x)  y=c(2+x)−1
$$\frac{\mathrm{dy}}{\mathrm{1}+\mathrm{y}}=\frac{\mathrm{dx}}{\mathrm{2}+\mathrm{x}} \\ $$$$\int\frac{\mathrm{dy}}{\mathrm{1}+\mathrm{y}}=\int\frac{\mathrm{dx}}{\mathrm{2}+\mathrm{x}} \\ $$$$\int\frac{\mathrm{d}\left(\mathrm{1}+\mathrm{y}\right)}{\mathrm{1}+\mathrm{y}}=\int\frac{\mathrm{d}\left(\mathrm{2}+\mathrm{x}\right)}{\mathrm{2}+\mathrm{x}} \\ $$$$\mathrm{ln}\:\left(\mathrm{1}+\mathrm{y}\right)=\mathrm{ln}\:\left(\mathrm{2}+\mathrm{x}\right)+\mathrm{ln}\:\mathrm{c}=\mathrm{ln}\:\mathrm{c}\left(\mathrm{2}+\mathrm{x}\right) \\ $$$$\mathrm{1}+\mathrm{y}=\mathrm{c}\left(\mathrm{2}+\mathrm{x}\right) \\ $$$$\mathrm{y}=\mathrm{c}\left(\mathrm{2}+\mathrm{x}\right)−\mathrm{1} \\ $$
Commented by tawakalitu last updated on 09/Dec/16
Thank you sir. God bless you.
$$\mathrm{Thank}\:\mathrm{you}\:\mathrm{sir}.\:\mathrm{God}\:\mathrm{bless}\:\mathrm{you}. \\ $$

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