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dy-dx-4y-x-1-2-x-




Question Number 90886 by jagoll last updated on 26/Apr/20
(dy/dx) −((4y)/x) = 1+(2/x)
$$\frac{{dy}}{{dx}}\:−\frac{\mathrm{4}{y}}{{x}}\:=\:\mathrm{1}+\frac{\mathrm{2}}{{x}} \\ $$
Answered by john santu last updated on 26/Apr/20
Commented by john santu last updated on 27/Apr/20
typo . y = ((∫ x^(−4) (1+(2/x))dx+C)/x^(−4) )  y = ((∫x^(−4) +2x^(−5) dx+C)/x^(−4) )  y=((−(1/3)x^(−3) −(1/2)x^(−4) +C)/x^(−4) )  y= Cx^4 −(1/3)x−(1/2)
$${typo}\:.\:{y}\:=\:\frac{\int\:{x}^{−\mathrm{4}} \left(\mathrm{1}+\frac{\mathrm{2}}{{x}}\right){dx}+{C}}{{x}^{−\mathrm{4}} } \\ $$$${y}\:=\:\frac{\int{x}^{−\mathrm{4}} +\mathrm{2}{x}^{−\mathrm{5}} {dx}+{C}}{{x}^{−\mathrm{4}} } \\ $$$${y}=\frac{−\frac{\mathrm{1}}{\mathrm{3}}{x}^{−\mathrm{3}} −\frac{\mathrm{1}}{\mathrm{2}}{x}^{−\mathrm{4}} +{C}}{{x}^{−\mathrm{4}} } \\ $$$${y}=\:{Cx}^{\mathrm{4}} −\frac{\mathrm{1}}{\mathrm{3}}{x}−\frac{\mathrm{1}}{\mathrm{2}} \\ $$
Commented by jagoll last updated on 27/Apr/20
thank you sir john
$${thank}\:{you}\:{sir}\:{john} \\ $$

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