a)
Select all solutions of (d^2/dx^2)y(x)+64y(x)=0.
y(x)=3cos(8x)
y(x)=3cos(4x)
y(x)=C1sin(8x)+C2cos(8x)
y(x)=−4sin(8x)
y(x)=C2cos(8x)
b)
Select all solutions of (d^2/dx^2)y(x)+36y(x)=0.
y(x)=C2cos(3x)
y(x)=C1sin(3x)
y(x)=3cos(3x)
y(x)=3cos(6x)
y(x)=3sin(3x)+8cos(3x)
Evaluate each integral using trig substitutions
1.) Integral of (3x^5dx)/(sqrt(16-x^2)
2.) Integral of (sqrt(x^2-16)dx)/x
3.) Integral of (6dx)/(16+16x^2)