Eliminating arbitrary constants

kindly help me with my homework. eliminate the following arbitrary constants...
y= x^2 + c1 e^3x + c2 e^3x.

Jhun Vert's picture

Are you sure that the power of e is the same for the 2nd and 3rd terms? Both are e3x.

In case if you mean y = x^2 + c1 e^2x + c2 e^3x:
$y = x^2 + c_1 e^{2x} + c_2 e^{3x}$   ←   Equation (1)

$y' = 2x + 2c_1 e^{2x} + 3c_2 e^{3x}$   ←   Equation (2)

$y'' = 2 + 4c_1 e^{2x} + 9c_2 e^{3x}$   ←   Equation (3)
 

Equation (2) - 3 × Equation (1)
$y' - y = (2x - 3x^2) - c_1 e^{2x}$   ←   Equation (4)

Equation (3) - 3 × Equation (2)
$y'' - y' = (2 - 6x) - 2c_1 e^{2x}$   ←   Equation (5)
 

Equation (5) - 2 × Equation (4)
$(y'' - y') - 2(y' - y) = (2 - 6x) - 2(2x - 3x^2)$ collect similar terms to get to your final answer.

thank you so much :)

Add new comment

Deafult Input

  • Allowed HTML tags: <img> <em> <strong> <cite> <code> <ul> <ol> <li> <dl> <dt> <dd> <sub> <sup> <blockquote> <ins> <del> <div>
  • Web page addresses and e-mail addresses turn into links automatically.
  • Lines and paragraphs break automatically.
  • Mathematics inside the configured delimiters is rendered by MathJax. The default math delimiters are $$...$$ and \[...\] for displayed mathematics, and $...$ and \(...\) for in-line mathematics.

Plain text

  • No HTML tags allowed.
  • Lines and paragraphs break automatically.