Question

Which one is the solution y(x) for the following ordinary differential equation and the specified boundary conditionmys?
$\frac{d^2y}{dx^2} -3 \frac{dy}{dx}+2y = 2e ^{-x}; y(0) =2; (\frac{dy}{dx}_{x=0})=1$

• A. $y(x)= \frac{1}{3}e^{-x} -2e^x- \frac1{3}e^{2x}$
• B. $y(x)= \frac{1}{3}e^{x} + 2e^x-\frac1{3}e^{2x}$
• C. $y(x)= \frac{1}{3}e^{-x} + 2e^{-x}-\frac1{3}e^{2x}$
• D. $y(x)= \frac{1}{3}e^{-x} + 2e^x-\frac1{3}e^{2x}$

Answer 1

Answer: (D)

$y(x)= \frac{1}{3}e^{-x} + 2e^x-\frac1{3}e^{2x}$

Answer 2

The correct answer is (C) : Inversion