Determine the order, degree, linearity, unknown function, and independent variable for the differential equations?
1. \(y \frac{d^{2} x}{d y^{2}}=\left(y^{2}\right)^{2}+1\)
2. \(5\left(\frac{d^{4} b}{d p^{4}}\right)^{5}+7\left(\frac{d b}{d p}\right)^{10}+b^{7}-b^{5}=p\)
3. \(5 \bar{y}+2 e^{t y}-3 y=t\)
4. \(t \ddot{y}+t^{2} \dot{y}-(\sin t) \sqrt{y}=t^{2}-t+1\)
5. \(y^{m \prime \prime}=\cos (2 t y)\)
Determine the order, degree, linearity, unknown function, and independent variable for the differential equations?
Determine the order, degree, linearity, unknown variable and independent variable of the following differential equations1. \(\frac{d y}{d x}=x y+3\)2. \(\frac{d^{2} y}{d x^{2}}+7 \frac{d y}{d x}+y=9\)3. \(\frac{d^{2} y}{d x^{2}}+7 \frac{d y}{d x}=\cos y \sin y\)4. \(x^{3} \frac{d^{2} y}{d x}+x^{2} \frac{d y}{d x}+x^{2} y=\sin x\)
Determine the order, degree, linearity, unknown function, and independent variable differential equations? y" = cos(2ty)
Problem 2- System Classification: Linearity (20pts) Circle all nonlinear terms (if any) in the following differential equations: (assume variables on left are outputs, at right are inputs) y'(t) *,4x, +4x, cos(x2) e. Problem 2- System Classification: Linearity (20pts) Circle all nonlinear terms (if any) in the following differential equations: (assume variables on left are outputs, at right are inputs) y'(t) *,4x, +4x, cos(x2) e.
Find \(\mathrm{dy} / \mathrm{dt}\).12) \(y=\cos ^{5}(\pi t-8)\)A) \(-5 \pi \cos ^{4}(\pi t-8) \sin (\pi t-8)\)B) \(-5 \cos ^{4}(\pi \mathrm{t}-8) \sin (\pi \mathrm{t}-8)\)C) \(5 \cos ^{4}(\pi t-8)\)D) \(-5 \pi \sin ^{4}(\pi t-8)\)Use implicit differentiation to find dy/dx.13) \(x y+x=2\)A) \(-\frac{1+y}{x}\)B) \(\frac{1+y}{x}\)C) \(\frac{1+x}{y}\)D) \(-\frac{1+x}{y}\)Find the derivative of \(y\) with respect to \(x, t\), or \(\theta\), as appropriate.14) \(y=\ln 8 x^{2}\)A) \(\frac{2}{x}\)B) \(\frac{1}{2 x+8}\)C) \(\frac{2 x}{x^{2}+8}\)D) \(\frac{16}{x}\)Find the derivative of \(\mathrm{y}\) with respect to \(\mathrm{x}, \mathrm{t}\), or \(\theta\), as appropriate.15) \(y=\left(x^{2}-2 x+6\right) e^{x}\)A)...
1-Given the function: \(y=\frac{x^{2}-3 x-4}{x^{2}-5 x+4}\), decide if \(f(x)=y\) is continuous or has a removable discontinuity, and find horizontal tond vertical asymptotes.2 A-Use the definition \(\lim _{h \rightarrow 0} \frac{f(x+h)-f(x)}{h}\) to prove that derivative of \(f(x)=\sqrt{4-x}\) is \(\frac{-1}{2 \sqrt{4-x}}\)2 B- Evaluate the limit \(\lim _{h \rightarrow 0} \frac{f(x+h) - f(x)}{h}\) for the given value of \(x\) and function \(f(x) .\)$$ f(x)=\sin x, \quad x=\frac{\pi}{4} $$3-Given the function: \(y=(x+4)^{3}(x-2)^{2}\), find y' and classify critical numbers very carefully using first derivative tess...
The IVP$$ \begin{array}{c} \sin (t) \frac{d^{2} x}{d t^{2}}+\cos (t) \frac{d x}{d t}+\sin (t) x=\tan (t) \\ x(0.75)=12 \\ \left.\frac{d x}{d t}\right|_{0,75}=2 \end{array} $$has a unique solution defined on the interval
1. For each of the following differential equations, state their order and if they are linear or nonlinear: (a) y" + sin(t)y = cos(t) (b) cos(t) + sin(y)t =y"
Determine whether the series converges or diverges.(1) \(\sum_{n=1}^{\infty} \frac{e^{1 / n}}{n^{2}}\)(2) \(\sum_{n=1}^{\infty}\left(\frac{2}{\sqrt{n}}+\frac{(-1)^{n}}{3^{n+1}}\right)\)(3) \(\sum_{n=1}^{\infty} \frac{5-2 \sin n}{n}\)(4) \(\sum_{n=1}^{\infty} \frac{3+\cos n}{n^{3 / 2}}\)(5) \(\sum_{n=0}^{\infty} \frac{\sqrt{n^{2}+2}}{n^{4}+n^{2}+5}\)(6) \(\sum_{n=1}^{\infty=1}\left(1+\frac{1}{n}\right)^{n}\)(7) \(\sum_{n=1}^{\infty} \frac{n+1}{n 2^{n}}\)(8) \(\sum_{n=1}^{\infty} \frac{\arctan n}{n^{4}}\)(9) \(\sum_{n=1}^{\infty} n \sin \frac{1}{n}\)
Determine the order of the given differential equations; also state whether the equation is linear or nonlinear. w (a). y = (sin t)y (b). (2 + y)y" – 4y = cos 3x.
Consider a system of differential equations describing the progress of a disease in a population, given byF, ) for a vector-valued function F. In our particular case, this IS. where z(t) is the number of susceptible individuals at time t and y(t) is the number of infected individuals at time t. The number of individuals is counted in units of 1,000 individuals a) Find the nullclines (simplest form) of this system of differential equations. The x-nullcline is y 2/3 The...