# Math Help - Differential equation and implicit mix- no idea

1. ## Differential equation and implicit mix- no idea

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.

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