How to Solve the Differential Equation dy/dx= x^2/y?

  • Context: Undergrad 
  • Thread starter Thread starter bilb27
  • Start date Start date
Click For Summary
SUMMARY

The differential equation dy/dx = x^2/y can be solved using separation of variables. By rearranging the equation, we obtain y dy = x^2 dx, which allows for integration on both sides. The solution involves integrating y with respect to dy and x with respect to dx, leading to the general solution y^2 = (1/3)x^3 + C, where C is the constant of integration. This method is essential for solving similar first-order differential equations.

PREREQUISITES
  • Understanding of first-order differential equations
  • Knowledge of separation of variables technique
  • Familiarity with integration methods
  • Basic algebra skills for manipulating equations
NEXT STEPS
  • Study the method of separation of variables in detail
  • Practice solving first-order differential equations
  • Explore integration techniques for various functions
  • Learn about the implications of the constant of integration in solutions
USEFUL FOR

Students in high school or undergraduate mathematics courses, educators teaching differential equations, and anyone interested in mathematical problem-solving techniques.

bilb27
Messages
1
Reaction score
0
Anyone help me with this please.

Solve the differential equation

dy/dx= x^2/y
 
Physics news on Phys.org
Hi bilb27, welcome to PF. If you click on the Rules tab above, you will find, among other things, this:

Homework Help:
On posting questions: Any and all high school and undergraduate homework assignments or textbook style exercises for which you are seeking assistance are to be posted in the appropriate forum in our Homework & Coursework Questions area--not in blogs, visitor messages, PMs, or the main technical forums. This should be done whether the problem is part of one's assigned coursework or just independent study. The reason for this is that the scientific and mathematical sections of Physics Forums are to be reserved for discussions and not academic assistance. Since graduate level assignments are meant to be more thought provoking (and hence more worthy of discussion), graduate level questions will be allowed in the relevant part of the main section of PF, provided that the graduate student attempts the problem and shows his work.

NOTE: You MUST show that you have attempted to answer your question in order to receive help. You MUST make use of the homework template, which automatically appears when a new topic is created in the homework help forums. Once your question or problem has been responded to, do not go back and delete (or edit) your original post.
 
http://www.wolframalpha.com/input/?i=dy%2Fdx%3D+x^2%2Fy
 

Similar threads

Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Direction Fields and Isoclines
  • · Replies 1 ·
Replies
1
Views
1K
Undergrad Expressing a differential equation into a different format
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Integral-form change of variable in differential equation
  • · Replies 1 ·
Replies
1
Views
2K
MHB -2.2.35 Show that dy/dx=(x+3y)/(x-y) is homogeneous. and....
  • · Replies 2 ·
Replies
2
Views
2K
Undergrad How do I solve this first order second degree differential equation?
  • · Replies 7 ·
Replies
7
Views
4K
Undergrad Solving Differential Equation Using Reduction of Order
  • · Replies 2 ·
Replies
2
Views
4K
MHB Solving a Separable Variable Differential Equation Using U-Substitution
  • · Replies 2 ·
Replies
2
Views
2K
MHB -b.2.2.1 separate variables y'=\dfrac{x^2}{y}
  • · Replies 4 ·
Replies
4
Views
2K
Undergrad Determining directional Field for say ##\dfrac{dy}{dx}=y-x##
  • · Replies 5 ·
Replies
5
Views
3K