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Category: Differential Equation

d-2-y-dx-2-2-dy-dx-y-3e-4x-y-0-2-3-dy-dx-x-0-13-3-

Question Number 157141 by cortano last updated on 20/Oct/21 $$\:\begin{cases}{\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }−\mathrm{2}\:\frac{{dy}}{{dx}}+{y}\:=\mathrm{3}{e}^{\mathrm{4}{x}} }\\{{y}\left(\mathrm{0}\right)=−\frac{\mathrm{2}}{\mathrm{3}}\:;\:\frac{{dy}}{{dx}}\mid_{{x}=\mathrm{0}} =\:\frac{\mathrm{13}}{\mathrm{3}}}\end{cases}\: \\ $$ Commented by john_santu last updated on 21/Oct/21 $$\:\begin{cases}{{y}''−\mathrm{2}{y}'+{y}=\mathrm{3}{e}^{\mathrm{4}{x}} }\\{{y}\left(\mathrm{0}\right)=−\frac{\mathrm{2}}{\mathrm{3}}\:;\:{y}'\left(\mathrm{0}\right)=\frac{\mathrm{13}}{\mathrm{3}}}\end{cases}…

y-y-

Question Number 157033 by amin96 last updated on 18/Oct/21 $${y}''=−{y} \\ $$ Commented by aliyn last updated on 19/Oct/21 $$\boldsymbol{{y}}^{''} \:+\boldsymbol{{y}}\:=\:\mathrm{0}\:\Rightarrow\:\left(\:\boldsymbol{{m}}−\boldsymbol{{i}}\right)\:\left(\boldsymbol{{m}}+\boldsymbol{{i}}\right)\:=\:\mathrm{0}\:\Rightarrow\:\boldsymbol{{m}}=\pm\boldsymbol{{i}} \\ $$$$ \\ $$$$\therefore\:\boldsymbol{{y}}\:=\:\boldsymbol{{c}}_{\mathrm{1}}…