# Separable Differential Equations

Printable View

• March 30th 2010, 08:40 AM
Spudwad
Separable Differential Equations
So I have been getting caught up on two separable differential equations the first being:

$\frac {3du} {dt} = u^2$ with initial conditions: $u(0) = 4$

I divided by $u^2$ and multiplied by $dt$ giving:

$\frac {3du} {u^2} = dt$ and after integrating I got:

$\frac {3} {u} +C = t + C$ and inversing it, so that the u was in the numerator and multiplying by 3 I ended up with:

$u = \frac {3} {t+c}$

But I am not sure if this is how the problem is really supposed to be done.

The other equation I am having trouble with is finding the general term for:

$\frac {dR} {dx} = a(R^2+25)$

where a is some nonzero constant. Would this just be $5tan(ax)+C$?

Thanks ahead of time for the help, I really appreciate it.
• March 30th 2010, 09:27 AM
mathemagister
Quote:

Originally Posted by Spudwad
So I have been getting caught up on two separable differential equations the first being:

$\frac {3du} {dt} = u^2$ with initial conditions: $u(0) = 4$

I divided by $u^2$ and multiplied by $dt$ giving:

$\frac {3du} {u^2} = dt$ and after integrating I got:

$\frac {3} {u} +C = t + C$ and inversing it, so that the u was in the numerator and multiplying by 3 I ended up with:

$u = \frac {3} {t+c}$

But I am not sure if this is how the problem is really supposed to be done.

The other equation I am having trouble with is finding the general term for:

$\frac {dR} {dx} = a(R^2+25)$

where a is some nonzero constant. Would this just be $5tan(ax)+C$?

Thanks ahead of time for the help, I really appreciate it.

$3\frac{du}{dt} = u^2$

$3u^{-2} du = dt$

Integrate:

$-3u^{-1} + K = t + K$

$\frac{-3}{u} = t + C$

$u = -\frac{3}{t+C}$

$u(0) = 4 \implies -\frac{3}{C}=4 \implies C = -\frac{3}{4}$

$u(t) = -\frac{3}{t-\frac{3}{4}}$
All times are GMT -8. The time now is 01:32 PM.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 25, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.960968554019928, "perplexity_flag": "middle"}