Diferrential Equation question

  • Thread starter Thread starter jofree87
  • Start date Start date
jofree87
Messages
37
Reaction score
0
Show that y= 1/(x2 - c) is a one parameter family of solutions of the differential equation dy/dx + 2xy2 = 0

This might sound like a stupid question, but am I just suppose to find the derivative of y and plug that into the differential equation and see if the solution is zero? Is that what they mean by "show"?
 
Physics news on Phys.org
I think that's exactly what they mean.
 

Thread 'Prove that the integral is equal to ##\pi^2/8##'

Prove $$\int\limits_0^{\sqrt2/4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx = \frac{\pi^2}{8}.$$ Let $$I = \int\limits_0^{\sqrt 2 / 4}\frac{1}{\sqrt{x-x^2}}\arcsin\sqrt{\frac{(x-1)\left(x-1+x\sqrt{9-16x}\right)}{1-2x}} \, \mathrm dx. \tag{1}$$ The representation integral of ##\arcsin## is $$\arcsin u = \int\limits_{0}^{1} \frac{\mathrm dt}{\sqrt{1-t^2}}, \qquad 0 \leqslant u \leqslant 1.$$ Plugging identity above into ##(1)## with ##u...
View full post »

Similar threads

How should I find the equilibrium points and the general equation?
Replies
3
Views
1K
Finding the rate of change of x in the equation
Replies
8
Views
1K
Relationship between autonomous system and related single equation
Replies
3
Views
2K
Simmons 7.10 & 7.11: Find Curves Intersecting at Angle pi/4
Replies
1
Views
2K
Why can't a critical point of a system of DEs be complex?
Replies
27
Views
2K
Question on Two Differentiation Techniques
Replies
25
Views
2K
Prove that solutions to autonomous first order DE can't have local maxima
Replies
2
Views
1K
Calculus ## G(y, z)=z\frac{\partial}{\partial z}F(y, z)-F(y, z) ##?
Replies
6
Views
2K
Confusion about the equation of a line in space (vector form)
Replies
23
Views
2K
Calculate this Integral around the Circular Path using Green's Theorem
Replies
3
Views
2K

Hot Threads

Recent Insights

Back
Top