 Recent questions in Differential equations
Differential equations
ANSWERED ### Find equations of both lines through the point (2, ?3) that are tangent to the parabola $$\displaystyle{y}={x}^{{2}}+{x}$$. $$\displaystyle{y}_{{1}}$$=(smaller slope quation) $$\displaystyle{y}_{{2}}$$=(larger slope equation)

Differential equations
ANSWERED ### Compute $$\displaystyle\triangle{y}$$ and dy for the given values of x and $$\displaystyle{\left.{d}{x}\right.}=\triangle{x}$$ $$\displaystyle{y}={x}^{{2}}-{4}{x},{x}={3},\triangle{x}={0},{5}$$ $$\displaystyle\triangle{y}=???$$ dy=?

Differential equations
ANSWERED ### Find an equation of the tangent line to the curve at the given point (9, 3) $$\displaystyle{y}={\frac{{{1}}}{{\sqrt{{{x}}}}}}$$

Differential equations
ANSWERED ### If $$\displaystyle{x}{y}+{8}{e}^{{y}}={8}{e}$$ , find the value of y" at the point where x=0 y"=?

Differential equations
ANSWERED ### Solve the differential equation by variation of parameters $$\displaystyle{y}\text{}{y}={\sin{{x}}}$$

Differential equations
ANSWERED ### Solve the given differential equation by separation of variables: $$\displaystyle{\frac{{{d}{P}}}{{{\left.{d}{t}\right.}}}}={P}-{P}^{{2}}$$

Differential equations
ANSWERED ### Find $$\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}$$ and $$\displaystyle{\frac{{{d}^{{2}}{y}}}{{{\left.{d}{x}\right.}^{{2}}}}}.{x}={e}^{{t}},{y}={t}{e}^{{-{t}}}$$. For which values of t is the curve concave upward?

Differential equations
ANSWERED ### Find the Exact length of the curve. $$\displaystyle{x}={e}^{{t}}+{e}^{{-{t}}},{y}={5}-{2}{t}$$ between $$\displaystyle{0}\leq{t}\leq{3}$$

Differential equations
ANSWERED ### Find the differential of each function. (a) $$y = \tan \sqrt{t}$$ (b) $$y= \frac{1-v^2}{1+v^2}$$

Differential equations
ANSWERED ### Can you indefinite the integral of $$\displaystyle{x}^{{2}}{\arcsin{{\left({x}\right)}}}$$ please?

Differential equations
ANSWERED ### $$\displaystyle{y}'={\left({y}+{4}{x}\right)}^{{2}}$$

Differential equations
ANSWERED ### $$\displaystyle{2}⋅{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}+{2}{y}={0}$$

Differential equations
ANSWERED ### When talking about boundary conditions for partial Differential equations, what does an open boundary mean?

Differential equations
ANSWERED ### $$\displaystyle{f{{\left({x}\right)}}}=\frac{{1}}{{1}}+{x}+{x}^{{2}}$$. find the maclaurin polynomial

Differential equations
ANSWERED ### $$\displaystyle\frac{{d^2y}}{{\left.{d}{x}\right.}^{{2}}}−{2}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}+{10}{y}={0}$$ where x=0.y=0 and $$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={4}?{x}={0}.{y}={0}$$ and $$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={4}$$?

Differential equations
ANSWERED ### $$\displaystyle{y}'={\left({y}+{4}{x}\right)}^{{2}}$$

Differential equations
ANSWERED ### $$\displaystyle{d}^{{2}}\frac{{y}}{{\left.{d}{x}\right.}^{{2}}}−{2}\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}+{10}{y}={0}$$ where $$x=0;y=0$$ and $$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={4}?{x}={0};{y}={0}$$ and $$\displaystyle\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}={4}$$?

Differential equations
ANSWERED ### In many physical applications, the nonhomogeneous term F(x) is specified by different formulas in different intervals of x. (a) Find a general solution of the equation $$\displaystyle{y}{''}+{y}=\left\{{x},{0}\leq{x}\leq{1},{1}\leq{x}\right\}$$ NoteNote that the solution is not differentiable at x = 1. (b) Find a particular solution of $$y''+y=\left\{x,0\leq x\leq 1;1,1\leq x\right\}$$ that satises the initial conditions y(0)=0 and y′(0)=1.

Differential equations
ANSWERED ### $$\displaystyle{2}⋅{\left(\frac{{\left.{d}{y}\right.}}{{\left.{d}{x}\right.}}\right)}+{2}{y}={0}$$
ANSWERED 