Find-the-value-of-constant-a-such-that-axe-x-is-a-solution-of-Differential-equation-d-2-y-dx-2-3-dy-dx-2y-2e-x-solve-D-E-for-which-y-1-and-dy-dx-3-when-x-0-

Tinku Tara June 3, 2023 Arithmetic 0 Comments

Question Number 77128 by peter frank last updated on 03/Jan/20

Find the value of constant “a” such that axe^(−x ) is a solution of Differential equation (d^2 y/dx^2 )+3(dy/dx)+2y=2e^(−x) solve D.E for which y=1 and (dy/dx)=3 when x=0

$${Find}\:{the}\:{value}\:{of}\:{constant} \\ $$$$“{a}''\:{such}\:{that}\:{axe}^{−{x}\:} {is} \\ $$$${a}\:{solution}\:{of}\:{Differential} \\ $$$${equation} \\ $$$$\frac{{d}^{\mathrm{2}} {y}}{{dx}^{\mathrm{2}} }+\mathrm{3}\frac{{dy}}{{dx}}+\mathrm{2}{y}=\mathrm{2}{e}^{−{x}} \\ $$$${solve}\:{D}.{E}\:{for}\:\:{which} \\ $$$${y}=\mathrm{1}\:{and}\:\frac{{dy}}{{dx}}=\mathrm{3}\:{when} \\ $$$${x}=\mathrm{0} \\ $$

Answered by peter frank last updated on 06/Jan/20