Solve IVP

{eq}12{y}''-21{y}'+9y=0 {/eq}

{eq}y(0)=12\\ {y}'(0)=-41/2 {/eq}

Question:

Solve IVP

{eq}12{y}''-21{y}'+9y=0 {/eq}

{eq}y(0)=12\\ {y}'(0)=-41/2 {/eq}

Differential Equation.

A differential Equation (D.E) has order and degree. The second order D.E is the equation consisting of double derivatives.

Solution to differential equation when the roots of its auxiliary equation is real and distinct is given by:

{eq}y = c_1e^{m_1t} + c_2 e^{m_2t}+ \cdot \cdot \cdot\\ {/eq}

where {eq}m_1,m_2,\cdot \cdot \cdot {/eq} are the roots of the auxiliary equation and {eq}c_1, c_2 {/eq} are the constants.

Answer and Explanation: 1

Become a Study.com member to unlock this answer!

View this answer

Given:

{eq}12{y}''-21{y}'+9y=0 {/eq}

The solution to the differential equation is given by:

{eq}y = y_c + y_p\,\, , where y_c {/eq} is the...

See full answer below.


Learn more about this topic:

Loading...
Differential Calculus: Definition & Applications

from

Chapter 13 / Lesson 6
15K

This lesson explores differential calculus. It defines a differential and delves into the many uses of differential equations.


Related to this Question

Explore our homework questions and answers library