Can you solve the question quickly please? dzyB: Solve the differential equation:dx2dy+3- 4y = x2dx

Answered: dzy d + 3- 4y = x? B: Solve the…

Calculus: Early Transcendentals

8th Edition

ISBN:9781285741550

Author:James Stewart

Publisher:James Stewart

Chapter1: Functions And Models

Section: Chapter Questions

Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...

See similar textbooks

Related questions

Question

Can you solve the question quickly please?

dzy
B: Solve the differential equation:
dx2
dy
+3- 4y = x2
dx

Expert Solution

Step 1

Given:

$\frac{d^{2} y}{d x^{2}} + 3 \frac{d y}{d x} - 4 y = x^{2}$ ...(1)

So, we can also write as:

$(D^{2} + 3 D - 4) y = x^{2}$

So, the auxiliary equation is:

$\begin{array}{rcl} m^{2} + 3 m - 4 & = & 0 \\ m^{2} + 4 m - m - 4 & = & 0 \\ m (m + 4) - 1 (m + 4) & = & 0 \\ (m + 4) (m - 1) & = & 0 \\ m & = & - 4, 1 \end{array}$

If roots of an auxiliary equation is real and distinct then the complimentary function is:

$C . F . = c_{1} e^{m_{1} x} + c_{2} e^{m_{2} x}$

So,

$C . F . = c_{1} e^{x} + c_{2} e^{- 4 x}$

Step by step

Solved in 2 steps

SEE SOLUTION Check out a sample Q&A here

Similar questions

Recommended textbooks for you

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781285741550

Author:

James Stewart

Publisher:

Cengage Learning

Thomas' Calculus (14th Edition)

Calculus

ISBN:

9780134438986

Author:

Joel R. Hass, Christopher E. Heil, Maurice D. Weir

Publisher:

PEARSON

Calculus: Early Transcendentals (3rd Edition)

Calculus

ISBN:

9780134763644

Author:

William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher:

PEARSON

Calculus: Early Transcendentals

Calculus

ISBN:

9781319050740

Author:

Jon Rogawski, Colin Adams, Robert Franzosa

Publisher:

W. H. Freeman

Precalculus

Calculus

ISBN:

9780135189405

Author:

Michael Sullivan

Publisher:

PEARSON

Calculus: Early Transcendental Functions

Calculus

ISBN:

9781337552516

Author:

Ron Larson, Bruce H. Edwards

Publisher:

Cengage Learning

SEE MORE TEXTBOOKS

dzy d + 3- 4y = x? B: Solve the differential equation: