b)\(\displaystyle{y}={\left\lbrace{x},{0}\leq{x}\leq{1};{1},{x}\leq{1}\right.}\)

Question

asked 2021-05-05

If \(f(x) + x^2[f(x)]^5 = 34\) and \(f(1) = 2,\) find \(f '(1).\)

asked 2021-06-02

If \(xy+8e^y=8e\) , find the value of y" at the point where \(x=0\)

\(y"=?\)

asked 2021-06-06

\(tf"(t)+f'(t)-f((t))^2=0\)

a) What is the order of this differential equation?

b) Show that \(f(t)=\frac{1}{t}\) is a particular solution to this differential equation.

c) Find a particular solution with \(f(0)=0\)

2. Find the particular solutions to the differential equations with initial conditions:

a)\(\frac{dy}{dx}=\frac{\ln(x)}{y}\) with \(y(1)=2\)

b)\(\frac{dy}{dx}=e^{4x-y}\) with \(y(0)=0\)

asked 2021-05-27

\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={z},{\frac{{{\left.{d}{z}\right.}}}{{{\left.{d}{x}\right.}}}}={F}{\left({x},{y},{z}\right)}.\)

Can something similar be done to the nth-order differential equation

\(\displaystyle{y}^{{{\left({n}\right)}}}={F}{\left({x},{y},{y}',{y}{''},\ldots,{y}^{{{\left({n}-{1}\right)}}}\right)}?\)