Question

(1 point) The general solution to the second-order differential equation 7y′′=4y′7y″=4y′ is in the form y(x)=c1erx+c2.y(x)=c1erx+c2. Find the value of r.

Answer 1

Answer:

$r=\frac{4}{7}\\\\General\,\,solution\,\,is\\\\y(x)=c_1e^{\frac{4}{7}x}+c_2$

Step-by-step explanation:

Given differential equation and its solution is

$7y''=4y'---(1)\\\\y(x)=c_1e^{rx} + c_2---(2)\\\\From\,\,(1)\\\\7D^2-4D=0\\\\D(7D-4)=0\\\\D=0\\\\D=\frac{4}{7}\\\\General\,\,solution\,\,is\\\\y_h(x)=c_1e^{\frac{4}{7}x}+c_2\\\\Comparing\,\,with\,\,(2)\\\\r=\frac{4}{7}$