Question
Find all values of $a$ such that $y=x^{a}$ is a solution of$$y^{\prime \prime}-12 x^{-2} y=0$$
Step 1
Step 1: First, we differentiate $y=x^{a}$ to get $y'=ax^{a-1}$ and $y''=a(a-1)x^{a-2}$. Show more…
Show all steps
Your feedback will help us improve your experience
Linh Vu and 76 other Calculus 2 / BC educators are ready to help you.
Ask a new question
Labs
Want to see this concept in action?
Explore this concept interactively to see how it behaves as you change inputs.
Key Concepts
Recommended Videos
Find all values of $a$ such that $y=e^{a x}$ is a solution of $$y^{\prime \prime}+4 y^{\prime}-12 y=0$$
INTRODUCTION TO DIFFERENTIAL EQUATIONS
Solving Differential Equations
Find all values of $a$ such that $y=e^{a x}$ is a solution of $$y^{prime prime}+4 y^{prime}-12 y=0$$
Find the particular solution indicated. $$ x y d x+2\left(x^{2}+2 y^{2}\right) d y=0 ; \text { when } x=0, y=1 $$
Equations of Order One
Equations with Homogeneous Coefficients
Transcript
Watch the video solution with this free unlock.
EMAIL
PASSWORD