Quiz 1 (Week 6): 2nd ODE

The standard form for 2nd order linear DE is

What is the order and degree of the differential equation?

• 1, 2
• 2, 1
• 3, 2
• 2, 3

Consider the following 2nd Order ODE $16\frac{\text{d}^2y}{\text{d}x^2}-40\frac{\text{d}y}{\text{d}x}+25y=0$  

Find the roots of equation and the general solution

• Roots = 2 and 3 (real and distinct).  $y\left(x\right)=e^x\left(A\cos2x+B\sin3x\right)$  

• Roots = 5/4 (complex roots).  $y\left(x\right)=e^x\left(A\cos2x+B\sin3x\right)$  

• Roots = 2 and 3 (real and distinct).  $y\left(x\right)=Ae^{2x}+Be^{3x}$  

• Roots = 5/4 (real & equal).  $y\left(x\right)=\left(A+Bx\right)e^{\frac{5}{4}x}$  

The nonhomogeneous 2nd order differential equation can be solved by

• separating the variables

• undetermined coefficient method

• variation of parameters method

• wronskian method

What is the general solution to the DE $\frac{\text{d}^2x}{\text{d}y^2}+7\frac{\text{d}x}{\text{d}y}-8y=0$  ?

•  $y=Ce^{-x}+De^{8x}$  

•  $y=Ce^x+De^{-8x}$  

•  $y=Ce^x+De^{7x}$  

•  $y=Ce^{-x}+De^{7x}$  

Find a general solution of the following homogeneous linear second order differential equation.

y "- 2 y '- 8 y=0

• y = c₁e^2x + c₂e^4x

• y= c₁e^-2x + c₂e^4x

• y = c₁e^2x + c₂e^-4x

• y = c₁e^-2x + c₂e^-4x