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CALCULUS AND ANALYSIS
DIFFERENTIAL EQUATIONS
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Recent Differential equations Answers
Recent questions in Differential equations
First order differential equations
asked 2021-03-07
Solve differential equation
\(\displaystyle{\frac{{{\left.{d}{y}\right.}}}{{{\left.{d}{x}\right.}}}}={\left({x}+{y}+{1}\right)}^{{2}}-{\left({x}+{y}-{1}\right)}^{{2}}\)
Laplace transform
asked 2021-03-07
Use the appropriate algebra and Table of Laplace's Transform to find the given inverse Laplace transform.
\(L^{-1}\left\{\frac{1}{(s-1)^2}-\frac{120}{(s+3)^6}\right\}\)
Laplace transform
asked 2021-03-07
Determine the Laplace transform of the given function f.
\(f(t)=(t -1)^2 u_2(t)\)
Laplace transform
asked 2021-03-07
use the Laplace transform to solve the initial value problem.
\(y"-3y'+2y=\begin{cases}0&0\leq t<1\\1&1\leq t<2\\ -1&t\geq2\end{cases}\)
\(y(0)=-3\)
\(y'(0)=1\)
First order differential equations
asked 2021-03-07
Solve differential equation
\(xu'(x)= u^2-4\)
First order differential equations
asked 2021-03-07
Solve differential equation
\(1+y^2+xy^2)dx+(x^2y+y+2xy)dy=0\)
First order differential equations
asked 2021-03-07
Solve differential equation
\(\frac{\cos^2y}{4x+2}dy= \frac{(\cos y+\sin y)^2}{\sqrt{x^2+x+3}}dx\)
Laplace transform
asked 2021-03-06
Find the laplace transform by definition.
a)
\(\displaystyle{L}{\left\lbrace{2}\right\rbrace}\)
b)
\(\displaystyle{L}{\left\lbrace{e}^{{{2}{t}}}\right\rbrace}\)
c)
\(\displaystyle{L}{\left[{e}^{{-{3}{t}}}\right]}\)
Laplace transform
asked 2021-03-06
Find the solution of the initial value problem given below by Laplace transform
\(y'-y=t e^t \sin t\)
\(y(0)=0\)
Differential equations
asked 2021-03-05
Solve differential equation:
\(\displaystyle{y}'+{y}^{{2}}{\sin{{x}}}={0}\)
Laplace transform
asked 2021-03-05
Find the laplace transform of the following:
\(a) t^2 \sin kt\)
\(b) t\sin kt\)
Laplace transform
asked 2021-03-05
Find the inverse Laplace Tranformation by using convolution theorem for the function
\(\frac{1}{s^3(s-5)}\)
First order differential equations
asked 2021-03-05
Solve differential equation
\(u'-5u=ve^(-5v)\)
First order differential equations
asked 2021-03-05
Solve differential equation
\(dy/dx -12x^3y = x^3\)
Laplace transform
asked 2021-03-04
use properties of the Laplace transform and the table of Laplace transforms to determine L[f]
\(f(t)=e^{3t}\cos5t-e^{-t}\sin2t\)
Laplace transform
asked 2021-03-04
use the Laplace transform to solve the given initial-value problem.
\(y"+y=f(t)\)
\(y(0)=0 , y'(0)=1\)
where
\(\displaystyle f{{\left({t}\right)}}={\left\lbrace\begin{matrix}{1}&{0}\le{t}<\frac{\pi}{{2}}\\{0}&{t}\ge\frac{\pi}{{2}}\end{matrix}\right.}\)
Laplace transform
asked 2021-03-04
Find the Laplace transformation (evaluating the improper integral that defines this transformation) of the real valued function f(t) of the real variable t>0. (Assume the parameter s appearing in the Laplace transformation, as a real variable).
\(f{{\left({t}\right)}}={2}{t}^{2}-{4} \cosh{{\left({3}{t}\right)}}+{e}^{{{t}^{2}}}\)
Laplace transform
asked 2021-03-02
use properties of the Laplace transform and the table of Laplace transforms to determine L[f]
\(f(t)=\int_0^t (t-w)\cos(2w)dw\)
Laplace transform
asked 2021-03-02
\(\text{Laplace transforms A powerful tool in solving problems in engineering and physics is the Laplace transform. Given a function f(t), the Laplace transform is a new function F(s) defined by }\)
\(F(s)=\int_0^\infty e^{-st} f(t)dt
\(\text{where we assume s is a positive real number. For example, to find the Laplace transform of } f(t)=e^{-t} \text{ , the following improper integral is evaluated using integration by parts:}
\(F(s)=\int_0^\infty e^{-st}e^{-t}dt=\int_0^\infty e^{-(s+1)t}dt=\frac{1}{s+1}\)
\(\text{ Verify the following Laplace transforms, where u is a real number. }\)
\(f(t)=t \rightarrow F(s)=\frac{1}{s^2}\)
Laplace transform
asked 2021-03-02
Solve the third-order initial value problem below using the method of Laplace transforms
\(y'''+3y''−18y'−40y=−120\)
\(y(0)=6\)
\(y'(0)=45\)
\(y"(0)=-21\)
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