Prove that a solution to the initial-value problemh(y) dydx = g(x), y(x0) = y0is defined

Chapter 8, Problem 68

(choose chapter or problem)

Prove that a solution to the initial-value problem

$h(y) \frac{d y}{d x}=g(x), y\left(x_{0}\right)=y_{0}$

is defined implicitly by the equation

$\int_{y_{0}}^{y} h(r) d r=\int_{x_{0}}^{x} g(s) d s$

Equation Transcription:

$h(y)\frac{dy}{dx}=g(x),\ y\left({{x}_{0}}\right)={y}_{0}$

∫ ${\ }_{{y}_{0}}^{y}h(r)dr$ $=$ ∫ ${\ }_{{x}_{0}}^{x}\ g(s)ds$

Text Transcription:

h(y)dy/dx=g(x), y(x_0)=y_0

Integral^y_y_0 h(r) dr = Integral^x_x_0 g(s) ds

Unfortunately, we don't have that question answered yet. But you can get it answered in just 5 hours by Logging in or Becoming a subscriber.

Login