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Category: Differential Equation

Question-183533

Question Number 183533 by MikeH last updated on 26/Dec/22 Commented by MikeH last updated on 26/Dec/22 $$\mathrm{please}\:\mathrm{guys}\:\mathrm{solve}\:\mathrm{using}\:\mathrm{the}\:\mathrm{method}\:\mathrm{undetermined} \\ $$$$\mathrm{coefficients}\:\mathrm{or}\:\mathrm{variation}\:\mathrm{of}\:\mathrm{parameters}. \\ $$ Answered by qaz last…

Question-183532

Question Number 183532 by MikeH last updated on 26/Dec/22 Answered by CElcedricjunior last updated on 26/Dec/22 $$\mathrm{3}\boldsymbol{{xy}}'−\boldsymbol{{y}}=\boldsymbol{{lnx}}+\mathrm{1}\:\:\:\:\boldsymbol{{y}}\left(\mathrm{1}\right)=−\mathrm{2} \\ $$$$\left(\boldsymbol{{h}}\right):\mathrm{3}\boldsymbol{{xy}}'−\boldsymbol{{y}}=\mathrm{0}=>\boldsymbol{{y}}=\boldsymbol{{e}}^{\int\frac{\mathrm{1}}{\mathrm{3}\boldsymbol{{x}}}\boldsymbol{{dx}}} =\boldsymbol{{ke}}^{\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{{ln}}\mid\boldsymbol{{x}}\mid} =\boldsymbol{{ke}}^{\frac{\mathrm{1}}{\mathrm{3}}\boldsymbol{{lnx}}} \boldsymbol{{pour}}\:\boldsymbol{{x}}\in\mathbb{R}_{+} ^{\ast} \\ $$$$\boldsymbol{{y}}=\boldsymbol{{k}}\sqrt[{\mathrm{3}}]{\boldsymbol{{x}}}…