Find all values of r for which the function y = e^(rx) satisfies the equation y'' + 5y'-6y=0

Q: 3. Given the equation y = x³ - 3x² + 3, determine all Critical Points and classify using the SECOND…

A:

Q: f(x, y) = ln (2x) In (3y) + x - y - xy - 3, then fyz (2,-) is equal to

A: Given :fx,y=ln2xln3y+x-y-xy-3

Q: y=8sin(x)cos(x) ; x=pi/3

A:

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: 1. Z= ;d'z/dx² 1+x2 2. Y (3x+2)* ;y" 3.…

A: 1) Given: Z=21+x2 Differentiating Z with respect to x, dZdx=2×ddx1+x2-1       =2×-11+x2-2×ddx1+x2…

Q: A curve passes through the point (2,0) has gradient dy at point (x, y) that satisfy the dx equation…

A:

Q: I FIND THE SECOND DERIVATIVE OF THE FF IN ITS SIMPLIFIED FORM 1. y Arctan- 3-V9-x2 2. y= 4 Arccos +…

A: 1.   From the given problem:   y=Arctanx3-9-x2   As we know:   d2ydx2=ddxdydx   So,…

Q: Compute the indicated derivative using the chain rule. x = 6 + 3t, y = −8t;  dy dx

A:

Q: first derivative y= 4in Gty) is dy 4.

A:

Q: 5. Find of the parameters: x = sin 2t and y = - cost at t = dx %3D

A: Topic = Derivative

Q: Find the derivative of the function y = (4x + 1)4(5x + 1)-5. dy (16x+4) 3 (4x+1)4 dx (5x+1)5…

A:

Q: usk 2: Find the derivative of 4x2 + 6y3 = 50 by filling the blanks. %3D (2 xD(x-)+x 6)(y³4)_=__ dy >…

A: We have, 4x2+6y3=50            ⋯⋯1 We know that, from basic derivative formula ddxkxn=n·kxn-1ddxk=0…

Q: Find y' by implicit differentiation 1. x²+4x-3y²+4y=0 2. 2xy+π sin y = 2π

A:

Q: 8. (x – 3y) dx + (3x – y) dy = 0; y(0) = 2

A: Homogeneous Differential Equation: A differential equation of the form f(x, y)dy = g(x, y)dx is said…

Q: Find the derivative of the function. rcos(x) y = In(1+2t)dt sin(x)

A: Applying Leibniz rule

Q: y = Arctan√3x−4/4 2. y = 2 Arccos ( 1 -x/2) + √4x − x2 3. y = ln (x3(x−1)/(x−2)^2) 4. y…

A: d2dx2arctan3x-44=d2dx2arctan3x-42=ddx1x3x-4=-9x-82x23x-43x-4…

Q: . Find P.S. of (16x +5y) dx + (3x+y) dy = 0 of the curre to pass thru the point (1,-3) 2. Find P.S.…

A:

Q: Obtain the derivative of the function y 4y sen (3x) – 7x In(2x + y) = e* - ey + 4tg(y)

A:

Q: Find dy/dx in terms of x and y if cos^2(9y)+sin^2(9y)=y+7 dy/dx=   implicit derivative problem.

A:

Q: To investigate these values, we find the second derivative f"(x) = %3D At the positive critical…

A: Given function is : fx=3x-4x3

Q: Usually in a method of solution for Homogeneous DE, after the substitution of y = vx (or x = vy) and…

A: In the method of solution for homogeneous differential equation, The equation is of the form,…

Q: dy cosx+ ysin x =1 dx

A:

Q: The derivative of y = 3cos(8x+6) is: 1. y' = 24 sin (8x+6) 2. y' = -24 sin (8x+6) 3. y' = -24 cos…

A:

Q: If we are getting the partial derivative of f(x,y) with respect to x, we are letting the y variable…

A: hello greetings from bartelby.i am here to help you.

Q: Find the second derivative of y = (4 – 2x)2 + 2sinx. dy Directly type your answer WITHOUT y' or dx…

A:

Q: Find dy/dx by implicit differentiation. 6,,3 x°y - y = x dy/dx

A: On implicit differentiation we differentiate both sides of the equation with respect to x . Then we…

Q: 11. Find the length of the curve x = on the interval (2, 4] (integrate with respect to y) 12y3 un

A: Given that the function x =y55+112y3 Find the arc length of the graph of the given curve on the…

Q: Find both first partial derivative Z = 15x x/y az az ду

A: As we know that: The the Power law: ddxxn=nxn-1 From the given problem: z=15xy

Q: 3. (x² – xy + y²)dx – xy dy = 0

A:

Q: 1 log3(r – y)*

A: Given; fx,y=1log3x-y   As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And…

Q: find a particular solution yp of the given equation. primes denote derivatives with respect to x.…

A:

Q: Find the derivative of y: 1- y = (cos 0)V2 Cos O 2- y = 7sec ln 7 3- y = 2sin 3t

A:

Q: Find a result by using homogenous for (x³ - 3x²y)dx-(x3³ - y³)dy = 0

A: This question is based on solution of Homogeneous differential equation.

Q: Find dy/dx by implicit differentiation. 5x3 + x2y − xy3 = 2

A:

Q: The population of a city is associated by the function P(x,y,z)=x² + 2y² + 2z². If the population of…

A:

Q: A heat-seeking particle is located at the point (2, 3) on a flat metal plate whose temperature at a…

A: A heat-seeking particle is located at the point 2,3 on a flat metal plate whose temperature at a…

Q: Find the linear approximation of the function f (x,y) = ln (x - 3y) at point (7,2).

A: To find the linear approximation of the function fx, y=lnx-3y at the point 7, 2.

Q: Find the derivative of 5e* 1. y = e 6x 3. y = 2x+3x 2. y = e* + e3x 4. y = (e* + ex)1/2

A: Quotient Rule of differentiation : ddxuv=v.dudx-dvdx.uv2 deaxdx=aeax dxndx=n.xn-1

Q: Give the integrating factor for 3((y^4)+1)dx+4x(y^3)dy=0. (in terms of x)

A:

Q: y" – 4y' +4y = 0; y(0) =-1, y'(0) = 0

A: We have to solve the differential equation…

Q: Find dy/dx by implicit differentiation. 5y sin(x2) = 9x sin(y2)

A: Given :  5y sin (x2) = 9x sin (y2)

Q: I FIND THE INDICATED DERIVATIVE IN ITS SIMPLIFIED FORM: (x2-3x)3 ; d'y/dx 1. y = 2. Y = (7x + 2)5…

A:

Q: Find y(1) for y" = - 4z - 4y, X, = 0, yo = 0, z, = 1, with step length 0.1 using Euler method (2nd…

A:

Q: 2. Find two positive numbers whose product is 750 and for which the sum of one and 10 times the…

A: Product of two numbers:= 750; Sum of one and 10times the other is minimum;

Q: Consider the function f(x) = x³ Q 2: Calculate its first derivative at point x = 3 numerically with…

A: We have given , f(x) = x3

Q: Use Leibniz’s Rule to find the derivatives of the functions

A: Given: y=∫x22x2lnt dt

Q: ry' = 3y + y? ху

A: Solution of a nonlinear differential equation

Q: 5. Implicitly differentiate the equation (xy)-y=x to find dx

A:

Q: Find the derivative of the function. 11) y = cos x4 A) dy -4 sin x 4 B) dY - sin x4 dx C) dy - -4x4…

A:

Q: 2- Find the derivative of y with respect to the Exercises 1-3. y = 6sinh ; 1- = - sinh (2x + 1) y =…

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.