calculus maths

posted by .

Hi can some one help, explain the following please. I seem to have issues with this:

1- Find the corresponding particular solution (in implicit form) that satisfies the initial; condition y = when x = 0.

2- Find the explicit form of this particular solution.

3- What is the value of y given by this particular solution when x =1? Give your answer to four decimal places.

regards Claire

• differential equations -

Take the example of a differential equation:

Since the differential equation in question has not been posted, I will work with an example.

y"-2y'+2y=e2x.....(1)

The solution yh to the homogeneous equation
y"-2y'+2y=0 .... (2)
is
yh=C1*ex+C2*x*ex

Note the two integration constants.

To obtain the general solution to equation (1), we must add to yh, solution of (2) a particular solution that satisfies (1). This is called a particular solution, yp.

For this particular problem,
yp=x²ex
which can be obtained by the method of variation of parameters.

Therefore the general solution of (1) is the sum of yh and yp, i.e.

y = C1*ex + C2*x*ex + x²ex ...(general solution)

However, y still contains the constants C1 and C2 to be determined. They can be found by the initial conditions, such as y(0)=0 and y'(0)=1.

Substitute (0,0) into the general solution, we obtain an equation in terms of C1 and C2.

Differentiate the general solution once and substitute x=0, y'(0)=1, we get another equation. From these equations, we can solve for C1 and C2 which is the solution to the problem.

The above general solution is explicit because y, and only y, appears only on the left hand side.

A solution of the form
xy²+x²=2y²
is called an implicit solution because y appears more than once in an equation.

Similar Questions

1. Maths

Hi I am really sorry I now people have already attempted to help me with this one already, however I am still not able to understand, I really have not done a lot of these equations and am struggling. I have put a little more information …
2. calculus

Please help. I have an implicit answer to a differential equation of 18y*sqrt(y)=(2(x^2-6x+23)^3/2)/3 plus arbitrary constant. What is the particular solution to this for which y=2 when x=1. And then express this particular solution …
3. calculus

Sorry to post this again, but I am still unable to understand it and need help. Please help.1) Using 3(x-3)(x^2-6x+23)^2 as the answer to differentiating f(x)=(x^2-6x+23)^3/2, which I have been able to do, I need to find the general …
4. Calculus

Find the particular solution that satisfies the intial condition: xdy - (2xe^(-y/x)+y)dx = 0
5. Calculus

Find a general solution to each first – degree ODE. If an initial condition is given, find the corresponding particular solution. Write all solutions explicitly if possible. dr/dè = r^(2)/è
6. Calculus

Find a general solution to each first ¨C degree ordinary differential equation. If an initial condition is given, find the corresponding particular solution. Write solution explicitly if possible. dx/dt=¡Ì(x+t+1)
7. Calculus-HELP PLZ !!!!

Find a general solution to the first – degree ODE. If an initial condition is given, find the corresponding particular solution. Write solution explicitly if possible. (9x^2+y-1)dx-(4y-x)dy=0, y(1)=0
8. Calculus-HELP!!!

Find a general solution to the first – degree ordinary differential equation. If an initial condition is given, find the corresponding particular solution. Write solution explicitly if possible: dx/dt=sqrt(x+t+1)
9. calculus

Find the particular solution that satisfies the differential equation and the initial condition. f ''(x) = x^2, f '(0) = 8, f(0) = 8 f (x) = ?
10. Calculus

Find the particular solution of differential equations that satisfies the initial condition dx/dy=e^(x+y) x(1)=0 I know you have to get all the y and dy on one side and x and dx on the other so you can intagrate and stuff, but im having …

More Similar Questions