Question
Asked Jun 28, 2019
2 views
3x2-3-4e2x and y(0) 8, then y=
If
dx
x3- 3x - 4e2x
x3- 3x - 2e2x + 8
x3- 3x - 2e2x
x3- 3x - 2e2x + 10
8A
help_outline

Image Transcriptionclose

3x2-3-4e2x and y(0) 8, then y= If dx x3- 3x - 4e2x x3- 3x - 2e2x + 8 x3- 3x - 2e2x x3- 3x - 2e2x + 10 8A

fullscreen
check_circle

Expert Answer

Step 1
help_outline

Image Transcriptionclose

The given differential equation is dy 3x2-3-4e* with y(0) = 8. dx Rewrite the given equation as dy (3x2-3-4e2)dx

fullscreen
Step 2
help_outline

Image Transcriptionclose

Integrate the equation dy = (3.x2 -3- 4e2*)dx on both sides to find y. fdy=[(3x° y3x* (3x2 -3-4e2*) dx (-4) das J(-3) dx + dx dx d dx n+1 x"dx -+C n1 1 -3(x)-4 e2x +C = 3 2 1 20) e'ds = e +C] and 4 x 3 - 3x 3 =x -3x- 2e2x+C Thus, the value of y = x'-3x-2e2* +C

fullscreen
Step 3
help_outline

Image Transcriptionclose

Use the initial condition y(0)=8 to find the value of C (0)-(0)x-2e2+C = 8 0-0-2e0C= 8 (=) -2 (1)C 8 -2 C 8 C 82 C 10 Substitute C 10 in y =x-3x -2e2* +C then y=x -3x -2e2*+10.

fullscreen

Want to see the full answer?

See Solution

Check out a sample Q&A here.

Want to see this answer and more?

Solutions are written by subject experts who are available 24/7. Questions are typically answered within 1 hour.*

See Solution
*Response times may vary by subject and question.
Tagged in

Math

Calculus

Integration

Related Calculus Q&A

Find answers to questions asked by student like you
Show more Q&A
add
question_answer

Q: This is solving the 2nd derivative of f(x) = x^2/ 1+e^x, and we have already obtained the 1st deriva...

A: The given function is,

question_answer

Q: 1) If an odd function h(x) has a local maximum value at x c, can anything be said about h at the val...

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

question_answer

Q: What is the solution to the initial value problem below? y′=5ex +8x3 +x2 +4x y(0)=3 Do not include "...

A: The given differential equation is, y′=5ex +8x3 +x2 +4x.

question_answer

Q: A port and a radar station are 3 mi apart on a straight shore running east and west. A ship leaves t...

A: Please look at thediagram on white board. I have used the diagram from the question itself and marke...

question_answer

Q: The funciton f in the figure satisfies the lim f(x)=5 as x approaches 4.  Determine the maximum valu...

A: (A) From the inequality |f(x)-5|<1 , we\'ll find range of f(x) first.

question_answer

Q: Calculate the directional derivative in the direction of v at the given point. fx, v)- tan Cy). -(1,...

A:  The partial derivatives of f(x,y) at the point (x,y)=(5,2)are:

question_answer

Q: The DeWitt Company has found that the rate of change of its average cost for product is C'(x)=(1/4)-...

A: Given information:The DeWitt Company has found that the rate of change of its average cost for produ...

question_answer

Q: I need step by step with explanations, because I turned my brain off and I’m having trouble turning ...

A: (a)The function is f(x) = sin4(4x5).

question_answer

Q: Help with #5

A: Given curve: r(t) = (2cost)i + (2sint)j + tkRecall the expressions for unit tanget and principal uni...