Differential equation and implicit mix- no idea

**kingkaisai2** · September 1st 2006, 07:02 PM

a. Two quantities x and y are related to each other by the differential equation ydy/dx=-16x. Solve this equation to get an implicit equation of the solution curve for which y=0 when x=0.1.

**Soroban** · September 1st 2006, 08:22 PM

Hello, kingkaisai2!

This is the simplest type: Variables Separable . . .

a. Two quantities $x$ and $y$ are related to each other
. . by the differential equation: $y\,\frac{dy}{dx} = -16x$

Solve this equation to get an implicit equation of the solution curve
. . for which $y=0$ when $x=0.1.$

We have: . $y\,dy \:=\:16x\,dx$

Integrate: . $\int y\,dy \:=\:\int 16x\,dx\quad\Rightarrow\quad \frac{1}{2}y^2\:=\:8x^2$ $+ c\quad\Rightarrow\quad y^2\:=\:16x^2 + C$

When $x = 0.1,\;y = 0:\;\;0^2 \:=\:16(0.1)^2 + C\quad\Rightarrow\quad C = -0.16$

Therefore: . $\boxed{y^2\;=\;16x^2 - 0.16}$

Thread: Differential equation and implicit mix- no idea

LinkBack

Thread Tools

Display

Differential equation and implicit mix- no idea

Similar Math Help Forum Discussions

No idea how to find this numerical value from this first order differential equation

No idea how to set up this equation

i've no idea to solve this equation..please help..urgent

No idea how to solve this differential equation

Differential equation in implicit form

Search Tags