y' - y = 16
To solve, rewrite the derivative as dy/dx .
(dy)/dx - y = 16
Then, express the equation in the form N(y)dy = M(x) dx .
(dy)/dx = y+16
(dy)/(y+16) = dx
Take the integral of both sides.
int (dy)/(y+16) = int dx
For the left side of the equation, apply the formula int (du)/u = ln|u|+C .
And for the right side, apply the formula int adx =ax + C.
ln |y+ 16| + C_1 = x + C_2
Then, isolate the y. To do so, move the C1 to the right side.
ln|y+16| = x + C_2-C_1
Since C1 and C2 represent any number, express it as a single constant C.
ln|y+16| = x + C
Then, convert this to exponential equation.
y+16=e^(x+C)
And, move the 16 to the right side.
y = e^(x+C) - 16
Therefore, the general solution is y = e^(x+C)-16 .
Tuesday, March 19, 2013
y'-y = 16 Solve the first-order differential equation
Subscribe to:
Post Comments (Atom)
Why is the fact that the Americans are helping the Russians important?
In the late author Tom Clancy’s first novel, The Hunt for Red October, the assistance rendered to the Russians by the United States is impor...
-
There are a plethora of rules that Jonas and the other citizens must follow. Again, page numbers will vary given the edition of the book tha...
-
The only example of simile in "The Lottery"—and a particularly weak one at that—is when Mrs. Hutchinson taps Mrs. Delacroix on the...
-
A good thesis statement presents a claim (an interpretive stance on a story that can be defended using textual evidence) and is a position w...
-
The given two points of the exponential function are (2,24) and (3,144). To determine the exponential function y=ab^x plug-in the given x an...
-
What does the hot air balloon symbolize? To the Assad son who buys the hot air balloon, it symbolizes a kind of whimsy that he can afford. B...
-
The play Duchess of Malfi is named after the character and real life historical tragic figure of Duchess of Malfi who was the regent of the ...
-
Allie’s baseball mitt is extremely important to Holden in The Catcher in the Rye. It is a symbol of Allie since it was important to his brot...
No comments:
Post a Comment