Solve second order DE

[esloveday]

Q: Solve d[sup:1znhvw4s]2[/sup:1znhvw4s]y/dx[sup:1znhvw4s]2[/sup:1znhvw4s]-3dy/dx+2y=0; y(0)=2, y'(0)=0

A: Unsure whether to use e[sup:1znhvw4s]x/2[/sup:1znhvw4s](Acos(sqrt(7)x)+Bsin(sqrt(7)x)) in which case is A=2 and B=0??

 

[galactus]

\(\displaystyle m^{2}-3m+2=0\)

\(\displaystyle m=2, \;\ m=1\)

\(\displaystyle Ce^{2x}+De^{x}\)

Using the initial conditions:

\(\displaystyle Ce^{2(0)}+De^{0}=2\)

\(\displaystyle 2Ce^{2(0)}+De^{0}=0\)

This gives two equations with two unknowns:

\(\displaystyle C+D=2, \;\ 2C+D=0\)

Solve for C and D.

This gives \(\displaystyle y=-2e^{2x}+4e^{x}\)

 

[esloveday]

Thankyou! Do you know of a good textbook or website that explains more of these types of problems?

 

[galactus]

Google