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Category: Differential Equation

How-can-we-solve-second-order-differential-equations-with-non-constant-coefficients-Any-idea-please-

Question Number 103266 by Ar Brandon last updated on 13/Jul/20 $$\mathrm{How}\:\mathrm{can}\:\mathrm{we}\:\mathrm{solve}\:\mathrm{second}-\mathrm{order}\:\mathrm{differential}\:\mathrm{equations}\:\mathrm{with} \\ $$$$\mathrm{non}-\mathrm{constant}\:\mathrm{coefficients}\:?\:\mathrm{Any}\:\mathrm{idea},\:\mathrm{please}\:? \\ $$$$ \\ $$ Commented by Ar Brandon last updated on 13/Jul/20…

y-4y-4y-e-2x-x-2-

Question Number 103203 by bobhans last updated on 13/Jul/20 $${y}''+\mathrm{4}{y}'+\mathrm{4}{y}\:=\:\frac{{e}^{−\mathrm{2}{x}} }{{x}^{\mathrm{2}} }\: \\ $$ Answered by bramlex last updated on 14/Jul/20 $$\mathrm{characteristic}\:\mathrm{eq}\: \\ $$$$\chi^{\mathrm{2}} +\mathrm{4}\chi+\mathrm{4}\:=\:\mathrm{0}\:;\:\left(\chi+\mathrm{2}\right)^{\mathrm{2}}…

how-to-solve-cos-30-sin-45-cos-30-dx-sin-45-dx-dx-dx-0-

Question Number 168663 by DomaPeti last updated on 15/Apr/22 $${how}\:{to}\:{solve}? \\ $$$$\frac{{cos}\left(\mathrm{30}°\right)\centerdot{sin}\left(\mathrm{45}°\right)−{cos}\left(\mathrm{30}°+{dx}\right)\centerdot{sin}\left(\mathrm{45}°+{dx}\right)}{{dx}}=? \\ $$$${dx}\rightarrow\mathrm{0} \\ $$ Commented by cortano1 last updated on 15/Apr/22 $$\underset{{dx}\rightarrow\mathrm{0}} {\mathrm{lim}}\frac{\frac{\mathrm{1}}{\mathrm{4}}\sqrt{\mathrm{6}}−\mathrm{cos}\:\left(\mathrm{30}°+{dx}\right).\mathrm{sin}\:\left(\mathrm{45}°+{dx}\right)}{{dx}}…

4x-2-y-y-0-x-gt-0-

Question Number 103037 by bramlex last updated on 12/Jul/20 $$\mathrm{4x}^{\mathrm{2}} \mathrm{y}''\:+\mathrm{y}\:=\:\mathrm{0}\:,\:\mathrm{x}\:>\:\mathrm{0} \\ $$ Answered by maths mind last updated on 12/Jul/20 $${let}\:{y}={x}^{{t}} \\ $$$$\Rightarrow\mathrm{4}{x}^{\mathrm{2}} \left({t}\left({t}−\mathrm{1}\right)\right){x}^{{t}−\mathrm{2}}…