y' + xy = 6x/y %3D (6+ Ce y= (6 + ce) = (6e+c)* - y = %3D 2 6+ Ce4 x² - y = %3D 2. . y%3D (6eT + C)

Q: What is initial value problem? Whey do you use initial condition in solving differential equations?

A: Solution: The initial value problem: An initial value peoblem is a differential equation together…

Q: Write the general solution if the ODE and its solutions are given as follows. y (4) + y" = 0 ;…

A:

Q: Determine the form of a particular solution yp of y" + 4y = x cosx. Do not solve the equation.

A: Given DE is y"+4y=xcosx .....(1) We find the form of particular solution yp.

Q: ty' + 2y = sint, y (π/2) = 1, t> 0

A: Given differential equation is ,        ty'+ 2y = sint      ;  yπ2=1 , t>0 (.)  Solution of a…

Q: Find the derivative of the trigonometric function. y = 8x cos(x) + x² sin(x) y' =

A: The given function is: y=8xcosx+x7sinx   As we know that; The Sum/difference rule: f±g'=f'±g' The…

Q: y (y - 2xy')² = 2 y'

A: Here, the differential equation is given by yy-2xy'2=2y'. Here, the differential equation has to be…

Q: 1. Consider the equation -xy"+y' + (x-1)y=0, x > 0. We can easily verify that y₁(x) = e* is a…

A: Given differential equation Also given that  is a solution of the given differential equation.Let…

Q: dy Solve the differential equation 3y² 6. dæ

A:

Q: Find the general solution of the differential equation 1 sin r y*y' + y*

A: The given equation is the first order differential equation:   Solve the differential equation by…

Q: et y" – 2y' + y = 1+ x2 -here y' = ) dy dx

A:

Q: Draw isoclines for the differential equation y' = 1+x-y and then choose which of the following…

A: Isoclines: The lines in the xy-plane in which the slope of the function is always same whatever be…

Q: solve the differential equation Lysiny 3

A: Introduction: A first-order differential equation of the form M(x,y)dx+N(x,y)=0 is known as the…

Q: Ordinary differential equation dx/dy = ( x-e-x )/( y+ey )

A: We can solve as follows

Q: 2. Solve (2x - 1)(y-1)dx + (x + 2)(x − 3)dy = 0; y(1) = -1

A:

Q: Find the general solution of each nonhomogeneous equation. y" + 2y' = 12t²

A:

Q: Solve differentials equation using method of variation parameters 3. x" + x = t cost + sint

A: Sol:- The given differential equation is: x" + x = t cos(t) + sin(t) The homogeneous equation…

Q: Classify the equation below according to the following Order: Degree: Types: Independent Variable:…

A: Concept: Equations with several unknown variables and their partial derivatives are known as partial…

Q: 1 fiel=r(e² + z² + ; 2-en )dz=? (e is the base of natural logarithm).

A: Let given integral is equal to I

Q: Solve the differential equation by variation of parameters. y" + 3y' + 2y = cos ex y(x) =

A: Given differential equation is y''+3y'+2y=cos ex The auxiliary equation is…

Q: With an assumption that an insect population grows continuously and the rate of growth is…

A:

Q: First order Linear DIFFERENTIAL EQUATION and Bernouli DIFFERENTIAL EQUATION

A: