# Calculus - Second Order Differential Equations

Solve the boundary-value problem.
y''+5y'-6y=0, y(0)=0, y(2)=1
r^2+5r-6=0, r1=1, r2=-6
y=c1*e^x + c2*e^-6x
y(x)=c1*e^x+c2*e^-6x
y'(x)=c1*e^x-6*c2*e^-6x
y(0)=c1+c2=0, c1=-c2
y(2)=c1*e^2+c2*e^(-12)=1
-c2*e^2-6c2*e^(-12)=1
-c2(e^2-6*e^-12)=1
c2=-1/(e^2-6e^-12)
c1=1/(e^2-6e^-12)
y(x)=(e^x)/(e^2-6*e^-12)+(6*e^-6x)/(e^2-6*e^-12)

Is this correct? Is there a way to further simplify this for y(x)? Thanks.

No. The second term has 6e^-6x in it, I don't see where the coefficent six came from. Testing it to the initial conditions, at x=0, y does not equal zero with that six in.

Oh, thank you for catching my mistake. I got the correct answer now. Thanks!

1. 👍 0
2. 👎 0
3. 👁 64

## Similar Questions

1. ### Calculus

Solve the boundary-value problem. y'' + 5y' - 6y = 0 , y(0) = 0 , y(2) = 1

asked by Sandy on March 16, 2014
2. ### geography

What is the difference between a Natural boundary and a political boundary? Give examples of each. A natural boundary something which separates things or places and is caused by geographic or physical items. A political boundary

asked by Reed on September 29, 2010
3. ### trigonometry

please help two boundary lines of a piece of property intersect at an angle 85 deg.. it is desired to cut off a triangular portion of the property which will be one acre (43560 sq. ft.) in area by means of a straight fence. If the

asked by josh on November 4, 2015
4. ### earth science

The deepest ocean trench is the Mariana trench. What is a contributing factor in it's depth? A. It is the site of an ancient meteorite collision. B. It is located near a divergent plate boundary. C. It is located near a convergent

asked by alz on October 24, 2018
5. ### Science

what is more like reverse faults, a convergent boundary or a transform boundary?

asked by Angie on March 4, 2009
6. ### maps

Is the shape of a state a political boundary or a natural boundary?

asked by Adam on February 9, 2009
7. ### Math

A landscape architect is designing a new park for the city.His design must include the following types of figures. Exactly 4 boundary segments Exactly 1 pair of boundary segments must be parallel The intersection of at least two

asked by Marina on March 9, 2017
8. ### maths

Let ABC be a triangle in the plane. Find circles C0;C1; : : : ;C6 such that Cj has exactly j points in common with the boundary of ABC (this \boundary" consists of the line segments AB, BC, CA). Is it possible to nd a circle C7

asked by jenny on October 12, 2012
9. ### College math

7) A rectangular pen can be constructed using the side of a barn as one boundary and 5500 ft. of fence to make the other three sides. Find the length and width of the rectangle to make the largest area. Hint: Draw a picture- and

asked by Michala on July 20, 2014
10. ### Child development

Using these steps, consider a cognitive “problem” a young child might encounter that he/she needs help with (such as putting together a puzzle, sequencing – putting items in order, sorting by color or size, adding,

asked by amy on October 14, 2011

More Similar Questions