Chapter 4: Q5RP (page 231)

Find a general solution to the given differential equation. $6 y'' - 11 y' + 3 y = 0$

Short Answer

Expert verified

The general solution to the given differential equation is $y = c_{1} e^{\frac{3}{2} t} + c_{2} e^{\frac{1}{3} t} .$

Step by step solution

Write the auxiliary equation of the given differential equation

The differential equation is $6 y'' - 11 y' + 3 y = 0 .$

The auxiliary equation for the above equation is $6 m^{2} - 11 m + 3 = 0 .$

Find the roots of the auxiliary equation

Solve the auxiliary equation,

$\begin{matrix} 6 m^{2} - 11 m + 3 = 0 \\ 6 m^{2} - 9 m - 2 m + 3 = 0 \\ 3 m (2 m - 3) - 1 (2 m - 3) = 0 \\ (2 m - 3) (3 m - 1) = 0 \end{matrix}$

The roots of the auxiliary equation are, $m_{1} = \frac{3}{2}, & m_{2} = \frac{1}{3} .$

Thus, the general solution of the given equation is $y = c_{1} e^{\frac{3}{2} t} + c_{2} e^{\frac{1}{3} t} .$

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Find a general solution to the given differential equation. $6 y'' - 11 y' + 3 y = 0$

Short Answer

Step by step solution

Write the auxiliary equation of the given differential equation

Find the roots of the auxiliary equation

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Find a general solution to the given differential equation.6y''-11y'+3y=0

Short Answer

Step by step solution

Write the auxiliary equation of the given differential equation

Find the roots of the auxiliary equation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Logic and Functions

Calculus

Statistics

Geometry

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Find a general solution to the given differential equation. $6 y'' - 11 y' + 3 y = 0$