Solve y(t)
Solve \(y(t)\) given
$$ y^{\prime}(t)+\int_{0}^{t} e^{2 \tau} y(t-\tau) d \tau=1, \quad y(0)=0 $$
Homework Answers
Solve the boundary value problem
Solve the boundary value problem $$ \begin{gathered} y^{\prime \prime \prime}=-\frac{1}{x} y^{\prime \prime}+\frac{1}{x^{2}} y^{\prime}+0.1\left(y^{\prime}\right)^{3} \\ y(1)=0 \quad y^{\prime \prime}(1)=0 \quad y(2)=1 \end{gathered} $$Use difference equations method. You can get help from matlab for solving the system.
Use the Laplace transform to solve the given initial-value problem.
Use the Laplace transform to solve the given initial-value problem.$$ y^{\prime}+y=f(t), \quad y(0)=0, \text { where } f(t)=\left\{\begin{array}{rr} 0, & 0 \leq t<1 \\ 5, & t \geq 1 \end{array}\right. $$
Find for the given F and C
Find \(\int_{C} \vec{F} \cdot d r\) for the given \(\vec{F}\) and \(C\).\(\cdot \vec{F}=-y \vec{i}+x \vec{j}+7 \vec{k}\) and \(C\) is the helix \(x=\cos t, y=\sin t r \quad z=t\), for \(0 \leq t \leq 2 \pi .\)$$ \int_{C} \vec{F} \cdot d \vec{r}= $$Find \(\int_{C} \overrightarrow{\mathrm{F}} \cdot d \overrightarrow{\mathrm{r}}\) for \(\overrightarrow{\mathrm{F}}=e^{y} \overrightarrow{\mathrm{i}}+\ln \left(x^{2}+1\right) \overrightarrow{\mathrm{j}}+\overrightarrow{\mathrm{k}}\) and \(C\), the circle of radius 4 centered at the origin in the \(y z\)-plane as shown below.$$ \int_{C} \vec{F} \cdot d \vec{r}= $$
1) Find the general solution of the given differential equation
1) Find the general solution of the given differential equationa) \(y^{\prime \prime}+2 y^{\prime}-3 y=0\),b) \(y^{\prime \prime}+3 y+2 y=0\),c) \(4 y^{\prime \prime}-9 y=0\),d) \(y^{\prime \prime}-9 y^{\prime}+9 y=0\).2) Find the solution of the given initial value problem and describe the behavior of solution as \(t \rightarrow+\infty\)$$ y^{\prime \prime}+4 y^{\prime}+3 y=0, \quad y(0)=2, y^{\prime}(0)=-1 $$3) Find a differential equation whose general solution is \(y=c_{1} e^{2 t}+c_{2} e^{-3 t}\).
value of z= 96 Task 3: Answer the following
value of z= 96Task 3: Answer the following:a. Evaluate: \(\int_{\frac{\pi}{2}}^{\pi} \boldsymbol{Z} \cos ^{3}(x) \sin ^{2}(x) d x\)b. The moment of inertia, \(I\), of \(a\) rod of mass ' \(m^{\prime}\) and length \(4 r\) is given by \(I=\int_{0}^{4 r}\left(\frac{Z m x^{2}}{2 r}\right) d x\) where \(^{\prime} x^{\prime}\) is the distance from an axis of rotation. Find \(I \)Task 4: Answer the following:Using the Trapezoidal rule, find the approximate the area bounded by the curve\(y=\boldsymbol{Z} e^{\left(\frac{x}{2}\right)}\), the \(\mathrm{x}\) -axis and coordinates \(x=0,...
Use the Laplace transform to solve the given system of differential equations.
Use the Laplace transform to solve the given system of differential equations.$$ \begin{aligned} &\frac{d x}{d t}=x-2 y \\ &\frac{d y}{d t}=5 x-y \\ &x(0)=-1, \quad y(0)=5 \end{aligned} $$
I have the first method complete, but I can't figure out thesecond method. I have...
I have the first method complete, but I can't figure out the
second method Could
someone please show how to use the second method?2. Find the unit step response of:$$ \begin{aligned} \dot{\overrightarrow{\mathbf{x}}}(t) &=\left[\begin{array}{cc} 0 & 1 \\ -2 & -2 \end{array}\right] \overrightarrow{\mathbf{x}}(t)+\left[\begin{array}{l} 1 \\ 1 \end{array}\right] u(t) \\ y(t) &=\left[\begin{array}{cc} 2 & 3 \end{array}\right] \overrightarrow{\mathbf{x}}(t) \end{aligned} $$by two methods (1): transfer function and then (2) \(y(t)=\mathbf{C} e^{\mathbf{A} t} \overrightarrow{\mathbf{x}}(0)+\mathbf{C} \int_{0}^{t} e^{\mathbf{A}(t-\tau)} \mathbf{B} u(\tau) d \tau+\mathbf{D} u(t)\). Re-member that the Laplace...
ZILLDIFFEQ9 11.1.016.
Let \(\left\{\varphi_{n}(x)\right\}\) be an orthogonal set of functions on \([a, b]\) such that \(\psi_{0}(x)=1\) and \(\varphi_{1}(x)=x\), Show that \(\int_{a}^{b}(\alpha x+\beta) \varphi_{n}(x) d x=0\) for \(n=2,3, \ldots\) and any constants \(\alpha\) and \(\beta\),First we note that \(\alpha x+\beta=(\square) \Phi_{1}(x)+(\square \quad) \Psi_{0}(x)\).Using this together with the fact that \(\varphi_{0}\) and \(\varphi_{1}\) are orthogonal to \(\varphi_{n}\) for \(n>1\), we have the following.$$ \begin{aligned} \int_{a}^{b}(\alpha x+\beta) \varphi_{n}(x) d x &=\int_{a}^{b} a x \psi_{n}(x) d x+\int_{a}^{b} \beta \varphi_{n}(x) d x \\ &=\int_{a}^{b}\left(\square_{0}\right) \varphi_{1}(x) \varphi_{n}(x) d...
Solve the given integral equation or integro-differential equation for y(t). t Y?) + 27 [(e-vycv y'...
Solve the given integral equation or integro-differential equation for y(t). t Y?) + 27 [(e-vycv y' (t) + 27 (t - Vy(v) dv = 5t, y(0) = 0 0 y(t) = 7
Problems 18 Solve the following ODEs using Laplace transforms: (a) + 23(t) _ у(t) _ 2y(t)' 0 give...
(a),(c),(d)
Problems 18 Solve the following ODEs using Laplace transforms: (a) + 23(t) _ у(t) _ 2y(t)' 0 given y(0) y(0) 0 and у(0) (b) y(t) + 43(t) + 4y(t)-v-t given y(0)-У(0) -0 (c) j;(t)-2ý(t) + y(t)--e2t given y(0) ,(0) -1 (d) a)+2) y) 3e-given y(0) 4,(0) 2 (e) y(t) + 2ý(t) + 2y(1) 5 sin t given y(0)-У(0)-: 0 (f) y(t) + 6)() + 9y(t) -121-e_3r given y(0) у(0) 0 6
Problems 18 Solve the following ODEs using Laplace...
Solve the boundary value problem $$ \begin{gathered} y^{\prime \prime \prime}=-\frac{1}{x} y^{\prime \prime}+\frac{1}{x^{2}} y^{\prime}+0.1\left(y^{\prime}\right)^{3} \\ y(1)=0 \quad y^{\prime \prime}(1)=0 \quad y(2)=1 \end{gathered} $$Use difference equations method. You can get help from matlab for solving the system.
value of z= 96Task 3: Answer the following:a. Evaluate: \(\int_{\frac{\pi}{2}}^{\pi} \boldsymbol{Z} \cos ^{3}(x) \sin ^{2}(x) d x\)b. The moment of inertia, \(I\), of \(a\) rod of mass ' \(m^{\prime}\) and length \(4 r\) is given by \(I=\int_{0}^{4 r}\left(\frac{Z m x^{2}}{2 r}\right) d x\) where \(^{\prime} x^{\prime}\) is the distance from an axis of rotation. Find \(I \)Task 4: Answer the following:Using the Trapezoidal rule, find the approximate the area bounded by the curve\(y=\boldsymbol{Z} e^{\left(\frac{x}{2}\right)}\), the \(\mathrm{x}\) -axis and coordinates \(x=0,...
I have the first method complete, but I can't figure out the
second method Could
someone please show how to use the second method?2. Find the unit step response of:$$ \begin{aligned} \dot{\overrightarrow{\mathbf{x}}}(t) &=\left[\begin{array}{cc} 0 & 1 \\ -2 & -2 \end{array}\right] \overrightarrow{\mathbf{x}}(t)+\left[\begin{array}{l} 1 \\ 1 \end{array}\right] u(t) \\ y(t) &=\left[\begin{array}{cc} 2 & 3 \end{array}\right] \overrightarrow{\mathbf{x}}(t) \end{aligned} $$by two methods (1): transfer function and then (2) \(y(t)=\mathbf{C} e^{\mathbf{A} t} \overrightarrow{\mathbf{x}}(0)+\mathbf{C} \int_{0}^{t} e^{\mathbf{A}(t-\tau)} \mathbf{B} u(\tau) d \tau+\mathbf{D} u(t)\). Re-member that the Laplace...
Let \(\left\{\varphi_{n}(x)\right\}\) be an orthogonal set of functions on \([a, b]\) such that \(\psi_{0}(x)=1\) and \(\varphi_{1}(x)=x\), Show that \(\int_{a}^{b}(\alpha x+\beta) \varphi_{n}(x) d x=0\) for \(n=2,3, \ldots\) and any constants \(\alpha\) and \(\beta\),First we note that \(\alpha x+\beta=(\square) \Phi_{1}(x)+(\square \quad) \Psi_{0}(x)\).Using this together with the fact that \(\varphi_{0}\) and \(\varphi_{1}\) are orthogonal to \(\varphi_{n}\) for \(n>1\), we have the following.$$ \begin{aligned} \int_{a}^{b}(\alpha x+\beta) \varphi_{n}(x) d x &=\int_{a}^{b} a x \psi_{n}(x) d x+\int_{a}^{b} \beta \varphi_{n}(x) d x \\ &=\int_{a}^{b}\left(\square_{0}\right) \varphi_{1}(x) \varphi_{n}(x) d...
Solve the given integral equation or integro-differential equation for y(t). t Y?) + 27 [(e-vycv y' (t) + 27 (t - Vy(v) dv = 5t, y(0) = 0 0 y(t) = 7
(a),(c),(d)
Problems 18 Solve the following ODEs using Laplace transforms: (a) + 23(t) _ у(t) _ 2y(t)' 0 given y(0) y(0) 0 and у(0) (b) y(t) + 43(t) + 4y(t)-v-t given y(0)-У(0) -0 (c) j;(t)-2ý(t) + y(t)--e2t given y(0) ,(0) -1 (d) a)+2) y) 3e-given y(0) 4,(0) 2 (e) y(t) + 2ý(t) + 2y(1) 5 sin t given y(0)-У(0)-: 0 (f) y(t) + 6)() + 9y(t) -121-e_3r given y(0) у(0) 0 6
Problems 18 Solve the following ODEs using Laplace...
Most questions answered within 3 hours.
-
are primates eutherians?
i know eutherians come from therians but does primates come from
eutharia bc...
asked 58 seconds from now -
Calculate the specific heat of a certain unknown metal, if it
requires 195 joules of heat...
asked 10 minutes ago -
Identify the characteristics of a successful
project.
Describe the phases the project lifecycle.
Define the roles...
asked 19 minutes ago -
1. In Module 2 "headers" and "footers" are
described. Explain the difference between them and how...
asked 14 minutes ago -
Three polarizing filters are stacked with the polarizing axes of
the second and third at 58.5...
asked 23 minutes ago -
The capacitance in a series RCL circuit is C1 = 3.3 μF, and
the corresponding resonant...
asked 33 minutes ago -
A 357.7-gram sample of an unknown substance (MM = 92.41 g/mol)
is heated from -23.1 °C...
asked 32 minutes ago -
The project aims to design a network for a casino. The casino
has 10 floors including...
asked 37 minutes ago -
Combustion of an unknown compound containing only carbon and
hydrogen produces 54.9 g of CO₂ and...
asked 52 minutes ago -
A basketball player achieves a hang time, the total time of
flight, of 0.748 s when...
asked 53 minutes ago -
A processor of carrots cuts the green top off each carrot,
washes the carrots, and inserts...
asked 1 hour ago -
Please help me find the coefficient of kinetic and static
friction of two masses (500kg and...
asked 1 hour ago