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# Recent Differential equations Answers # Recent questions in Differential equations

Differential equations asked 2020-11-12

### $$F(x) = (lnx)^{\cos}x,$$ find f'(x) and the equation to the tangent line at (e 1)

First order differential equations asked 2020-11-10

### Solve differential equation $$\displaystyle{y}'+{y}{\cot{{\left({x}\right)}}}={\sin{{\left({2}{x}\right)}}}$$

Laplace transform asked 2020-11-10

### Solve by Laplace transforms $$y"-3y'+2y=2\delta(t-1)$$ $$y(0)=1$$ $$y'(0)=0$$

Laplace transform asked 2020-11-10

### use the Laplace transform to solve the given initial-value problem. $$y"-3y'+2y=4 \ , \ y(0)=0 \ , \ y'(0)=1$$

First order differential equations asked 2020-11-10

### Find the sokaton 02 the ger Initial value provsem. $$y′−y=8t2,y(0)=1$$

First order differential equations asked 2020-11-10

### Solve differential equation $$(2y-e^x)dx+xdy=0$$, x>0

Differential equations asked 2020-11-09

### solve the Differential equations $$\displaystyle{y}{'''}+{10}{y}{''}+{25}{y}'={0}$$

Second order linear equations asked 2020-11-09

### Solve for the general solution of the given special second-ordered differential equation $$xy''+x(y')^2-y'=0$$

Second order linear equations asked 2020-11-09

### Let $$y_1$$ and $$y_2$$ be solution of a second order homogeneous linear differential equation $$y''+p(x)y'+q(x)=0$$, in R. Suppose that $$y_1(x)+y_2(x)=e^{-x}$$, $$W[y_1(x),y_2(x)]=e^x$$, where $$W[y_1,y_2]$$ is the Wroian of $$y_1$$ and $$y_2$$. Find p(x), q(x) and the general form of $$y_1$$ and $$y_2$$.

Laplace transform asked 2020-11-09

### Find x(t) and Y(t) using Laplace transform. $$\begin{cases} \frac{dx}{dt}=2x-3y \frac{dy}{dt}=y-2x \end{cases}$$ $$x(0)=8 , y(0)=3$$

Laplace transform asked 2020-11-09

### determine the inverse Laplace transform of the function. $$\displaystyle{Q}{\left({s}\right)}=\frac{s}{{{s}^{2}+{64}}}$$

Laplace transform asked 2020-11-09

### Use Laplace transform to evaluate the integral $$\int_0^\infty te^{-2t} \sin(2t)dt$$ a) $$\frac{1}{B}$$ b) not defined c) $$\frac{4s}{(s^2+4)^2}$$ d) $$\frac{4(s+2)}{(s^2+4s+8)^2}$$

Laplace transform asked 2020-11-09

### Solve the third-order initial value problem below using the method of Laplace transforms $$y'''-2y"-21y'-18y=-18$$ $$y(0)=2$$ $$y'(0)=7$$ $$y"(0)=95$$

Laplace transform asked 2020-11-09

### Solve the inital value problem by using Laplace transform: $$y''-5y'+6y=-8\cos(t)-2\sin(t), y(\frac{\pi}{2})=1 ,y'(\frac{\pi}{2})=0$$

First order differential equations asked 2020-11-09

### Solve differential equation $$xy'= 6y+12x^4 y^(2/3)$$

Differential equations asked 2020-11-08

### A particle moves along the curve $$\displaystyle{x}={2}{t}^{{2}}{y}={t}^{{2}}-{4}{t}$$ and z=3t-5 where t is the time.find the components of the velocity at t=1 in the direction i-3j+2k

Laplace transform asked 2020-11-08

### How to solve this equation $$y'''-4y"+2y'-16y=4x+1$$ using Method of Undetermined Coefficient, Variation of Parameters and Laplace Transformation

Laplace transform asked 2020-11-08

### Given that $$f{{\left({t}\right)}}={4}{e}^{{-{3}{\left({t}-{4}\right)}}}$$ a) Find $${L}{\left[\frac{{{d} f{{\left({t}\right)}}}}{{{\left.{d}{t}\right.}}}\right]}$$ by differentiating f(t) and then using the Laplace transform tables in lecture notes. b) Find $${L}{\left[\frac{{{d} f{{\left({t}\right)}}}}{{{\left.{d}{t}\right.}}}\right]}$$ using the theorem for differentiation c) Repeat a) and b) for the case that $$f{{\left({t}\right)}}={4}{e}^{{-{3}{\left({t}-{4}\right)}}}{u}{\left({t}-{4}\right)}$$

Laplace transform asked 2020-11-08

### Given the function $$\begin{cases}e^{-t}& \text{if } 0\leq t<2\\ 0&\text{if } 2\leq t\end{cases}$$ Express f(t) in terms of the shifted unit step function u(t -a) F(t) - ? Now find the Laplace transform F(s) of f(t) F(s) - ?

Laplace transform asked 2020-11-08

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