Active forum topics
- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Eliminate the Arbitrary Constants
- Law of cosines
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Integration of 4x^2/csc^3x√sinxcosx dx
- application of minima and maxima
- Sight Distance of Vertical Parabolic Curve
- Application of Differential Equation: Newton's Law of Cooling
New forum topics
- General Solution of $y' = x \, \ln x$
- engineering economics: construct the cash flow diagram
- Integration of 4x^2/csc^3x√sinxcosx dx
- Maxima and minima (trapezoidal gutter)
- Special products and factoring
- Newton's Law of Cooling
- Law of cosines
- Can you help me po to solve this?
- Eliminate the Arbitrary Constants
- Required diameter of solid shaft
Recent comments
- Hello po! Question lang po…1 week 3 days ago
- 400000=120[14π(D2−10000)]
(…1 month 2 weeks ago - Use integration by parts for…2 months 1 week ago
- need answer2 months 1 week ago
- Yes you are absolutely right…2 months 2 weeks ago
- I think what is ask is the…2 months 2 weeks ago
- $\cos \theta = \dfrac{2}{…2 months 2 weeks ago
- Why did you use (1/SQ root 5…2 months 2 weeks ago
- How did you get the 300 000pi2 months 2 weeks ago
- It is not necessary to…2 months 2 weeks ago
Do you mean eliminate c1, c2,
Do you mean eliminate c1, c2, and c3 from this equation: y = c1e5x + c2x + c3? If so, this is my solution to it:
$y = c_1 e^{5x} + c_2 x + c_3$
$y' = 5c_1 e^{5x} + c_2$
$y'' = 25c_1 e^{5x}$
$y''' = 125c_1 e^{5x}$
$y''' - 5y'' = 0$ ← this is my answer.
Do you have answer key to this problem? If you do, update us.
$$ \begin{eqnarray}
$$ \begin{eqnarray}
y &=& c_1 e^{5x} + c_2 x + c_3\\
y' &=& 5c_1e^{5x} + c_2\\
y'' &=& 25c_1e^{5x}\\
e^{-5x} y'' &=& 25c_1\\
e^{-5x} y''' - 5e^{-5x} y'' &=& 0 \\
y''' - 5y'' &=& 0
\end{eqnarray} $$
The second to the last line is done by taking a derivative. The 4th line was from the division of $e^{5x}$ so that the constant is isolated at the right hand side for it to be eliminated immediately after taking a derivative.
My answer is also $$\boxed{y''' - 5y'' = 0}$$