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Question Number 182139 by Mastermind last updated on 04/Dec/22

$$\mathrm{Find}\mathrm{constant}\mathrm{a},\mathrm{b},\mathrm{so}\mathrm{that}$$$$\mathrm{y}\left(\mathrm{t}\right)=(\mathrm{t}+3){\mathrm{e}}^{2\mathrm{t}}\mathrm{is}\mathrm{solution}\mathrm{of}\mathrm{IVP}$$$${\mathrm{y}}^{{}^{\prime }}=\mathrm{ay}+{\mathrm{e}}^{2\mathrm{t}},\mathrm{y}\left(0\right)=\mathrm{b}$$$$$$$$.$$

Commented by mr W last updated on 06/Dec/22

$$doyounevergiveafeedbackwhena$$$$questionofyoursisanswered?$$

Answered by mr W last updated on 04/Dec/22

$$y^{\prime }=e^{2t}+2(t+3)e^{2t}$$$$e^{2t}+2(t+3)e^{2t}=a(t+3)e^{2t}+e^{2t}$$$$\Rightarrow 2=a$$$$y\left(0\right)=(0+3)e^0=3=b$$

Commented by Mastermind last updated on 22/Dec/22

$$\mathrm{Thank}\mathrm{you}\mathrm{boss}$$

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