Question

Consider the differential equation \[ \frac{d^{2}y}{dx^{2}}+3\frac{dy}{dx}+2y=0 \] with the conditions \(y(0)=20\) and \(y'(0)=10\). Then, the value of \[ y(1)e^{2}-50e+20= \] is

• A. \(30\)
• B. \(0\)
• C. \(-30\)
• D. \(-10\)

Hint:

For second-order homogeneous differential equations: \[ \boxed{ am^2+bm+c=0 } \] Find the roots first, write the complementary solution, then use the initial conditions to determine the constants.

Answer 1

The Correct Option is D