# 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.

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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...