University Math / Homework Help. Derivative of dy/dx will equal to d^2y/dx^2 -called 2nd derivative of y with respect to x. I am somewhat confused on this lesson, please help!
Let y=a .e^mx ,so dy/dx =a.me^mx and d^2y/dx^2 = a m^2 e^mx ; then d^2y/dx^2+2dy/dx +y =a,(m^2+2m+1).e^mx =0 , e^mx not equal to zero then m^2+2m+1=0 or (m+1)^2=0 ,so m=-1 , Therefore y=a.e^(-x) + C [C is the constant of integration] is the general solution of the given differential equation. Then again take derivative this. I'll admit, I had to pick my old semester books apart to find the method, but in the end!
0 0 0. Singular solution is a solution where there is an absence of arbitrary constants. Dy/DX=1. *A: The given Bernoulli’s equation can be written as:A: According to the given information,For part (a)Consider a vector field A as:Q: Solve the bernoulli's equationx(6x^2−y−1)dy +2ydx =0.Q: A group of 150 tourists planned to visit East Africa. d^2y/dx^2 is the 2nd derivative so you just differentiate the above answer so it equals=-2. Find any inflectio...Q: a) For the given a vector field A = 3x*yz a, + x*z a,+ (x*y – 2z) a, check whether givenvector 'A' ...Q: Use the inverse differential operators to solve the initial value problem:2y'' + 5y' + 2y = e2xQ: 3. 1 Answer. Y=x. If so, dy/dx = 2, and d^2y/dx^2 = 0 (dx/dy = 1/2, since x = [ 1/2 ]y - 1/2) Positive: 0 % Answer #5 | 06/10 2016 08:18 example. All rights reserved.from GRE Math: Study Guide & Test PrepFind the complementary function: y = 2x^2 + 3. dy/dx = 4x. Let y=a .e^mx ,so dy/dx =a.me^mx and d^2y/dx^2 = a m^2 e^mx ; then d^2y/dx^2+2dy/dx +y =a,(m^2+2m+1).e^mx =0 , e^mx not equal to zero then m^2+2m+1=0 or (m+1)^2=0 ,so m=-1 , Therefore y=a.e^(-x) + C [C is the constant of integration] is the general solution of the given differential equation. (dy/dx)^2 = (dy/dx) (dy/dx) which as you can see is not the same thing as the second derivative: d^2 y /dx^2 = d/dx (dy/dx) 0 0 0. This is the difference between them If you want any speci...Q: Find the open intervals where the function is concave upward or concave downward.
0 2 2. They are not the same (dy/dx)^2 means the square of the first derivative. \\ \begin{align*} C.F &= A^{\alpha x} ( A \cos \beta x + B \sin \beta x) \\ C.F &= A \cos 4 x + B \sin 4 x & (\text{Where} \ \alpha = 0 \ \text{and} \ \beta = 4) \end{align*} {/eq}{eq}\text{To find the complementary function first we have to change the equation into auxiliary equation}. Login to reply the answers Post; guyava99. \\ \text{We have to compare with some cases to find the complementary function}. Hence, this is actually just a first-order equation in disguise. asked Dec 19, 2019 in Limit, continuity and differentiability by Vikky01 (41.7k points) d 2 x/dy 2 equals (A) (d 2 y/dx 2)-1 (B) - (d 2 y/dx 2)-1 (dy/dx)-3 (C) (d 2 y/dx 2)(dy/dx)-2 (D) - (d 2 y/dx 2)(dy/dx)-3. differentiation; jee; jee mains; Share It On Facebook Twitter Email. Q: Please do not use particular methodSolutions are written by subject experts who are available 24/7.
d^2x/dy^2 equals (A) (d^2y/dx^2)^-1 ← Prev Question Next Question → 0 votes . Thread starter ceity; Start date Jan 20, 2014; Tags d2y or dx2; Home. C. ceity. 9 years ago. {eq}\displaystyle \frac{d^2y}{dx^2} + 16y = 0 {/eq} Complementary Function: {eq}\text{To find the complementary function first we have to change the equation into auxiliary equation}. Do you know what's a derivative? Calculus . Forums. Means (Dy/DX)^2=(1)^2=1. Login to reply the answers Post; Demiurge42. d^2y/dx^2 = 4 (dy/dx)^2 = (4x)^2 = 16x^2. Questions are typically answered within 1 hour. All other trademarks and copyrights are the property of their respective owners. (1) . The first derivative is dy/dx = -2x . Again dy/dx =2 ,so dy/dx = a.me^mx +0 =2 … Solution for Solve dy/dx=2xy/(x^2-y^2) Q: A group of 150 tourists planned to visit East Africa.
\\ \text{We have to know three cases}: \\ \text{Case (i)}: \\ \text{The roots are real and different} \\ {\color{black}{C.F = Ae^{m_{1}x} + Be^{m_2x}}} \\ \text{Case (ii):} \\ \text{The roots are real and equal}: \\ {\color{black}{C.F = (A + Bx) e^{mx}}} \\ \text{Case (iii)}: \\ \text{The roots are Imaginary}: \\ {\color{black}{C.F = e^{\alpha x} (A \cos \beta x + B \sin \beta x)}} {/eq}{eq}\displaystyle \frac{d^2y}{dx^2} + 16y = 0 {/eq}Our experts can answer your tough homework and study questions.© copyright 2003-2020 Study.com. Lv 7. Among them, 3 fall ill and did not come, of th...A: Hey, since there are multiple questions posted, we will answer first question. x^2 - y^2 = -15 If I knew how to find the 2nd derivative, I could figure out the rest... fysmat. Jan 2014 19 0. {eq}\boxed{\text{The solution is} \ {\color{Blue}{ C.F = \displaystyle A \cos 4 x + B \sin 4 x }}} {/eq}{eq}{\color{Black}{\text{Solution}}}: \\ \text{Given}: \\ \displaystyle \frac{d^2y}{dx^2} + 16y = 0 \\ \text{To find the complementary function, first we have to change this equation into auxiliary equation}: \\ \text{The auxiliary equation is}: \\ \displaystyle m^2 + 16 = 0 \\ \text{To find the C.F we have to find the roots}: \\ m^2 = - 16 \\ m = \pm \sqrt{ - 16} \\ m = \pm 4i \\ \text{Therefore, the roots are imaginary.} D^2y/dx^2 means 2 time derivative and (Dy/DX )^2 means 1 times derivative and square of 1 time derivative.