Solving Differential Equation: xy' + y = sqrt(x-1)

Click For Summary
SUMMARY

The discussion focuses on solving the differential equation xy' + y = sqrt(x-1). The participant expresses difficulty in solving the equation due to their familiarity only with separable differential equations. A key insight provided is the necessity of using integrating factors to solve this type of differential equation, which is essential for transforming it into a solvable form.

PREREQUISITES
  • Understanding of differential equations, specifically first-order linear equations.
  • Familiarity with the concept of integrating factors in differential equations.
  • Knowledge of separable differential equations and their solutions.
  • Basic calculus skills, including integration techniques.
NEXT STEPS
  • Study the method of integrating factors for first-order linear differential equations.
  • Practice solving various forms of differential equations, including non-separable types.
  • Learn about the general solution of linear differential equations.
  • Explore advanced techniques in differential equations, such as Laplace transforms.
USEFUL FOR

Students and educators in mathematics, particularly those studying differential equations, as well as anyone seeking to enhance their problem-solving skills in this area.

Dell
Messages
555
Reaction score
0
i just started a course in differential equations, and this question was in the homework that i got, I am not sure we learned how to solve it but maybe i am meant to know.

xy' + y = sqrt(x-1)

up until now all i have been able to solve is equations which i can bring to a form of dx/x +dy/y = 0 or something like that

because this question has 3 parts i haven't been able to get F(x)dx + F(y)dy=0

xy' + y = sqrt(x-1)

x*dy/dx + y =sqrt(x-1)

dy/y + x*dx = sqrt(x-1)*dx/y

dy/y = (sqrt(x-1)/y - x )dx

now i can't integrat this because on the right i have y as well as x and cannot get rid of it
 
Physics news on Phys.org
Looks like you are familiar only with separable differential equations. Have you learned about integrating factors? That's what you need to solve this DE.
 

Similar threads

Finding the rate of change of x in the equation
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad Integral confusion for a simple Differential Equation
  • · Replies 2 ·
Replies
2
Views
2K
Volume between a region (above x-axis and below parabola) and a surface
  • · Replies 4 ·
Replies
4
Views
3K
Relationship between autonomous system and related single equation
  • · Replies 3 ·
Replies
3
Views
2K
Undergrad Integral-form change of variable in differential equation
  • · Replies 1 ·
Replies
1
Views
2K
Undergrad Closed implies exact (differential 1-forms on R^2)
  • · Replies 6 ·
Replies
6
Views
4K
Undergrad Why Lagrange’s method of solving Pp + Qq=R works?
  • · Replies 3 ·
Replies
3
Views
2K
How should I find the equilibrium points and the general equation?
  • · Replies 3 ·
Replies
3
Views
2K
Understanding Equlibrium Points in differential equations
  • · Replies 9 ·
Replies
9
Views
2K
Calculus ## G(y, z)=z\frac{\partial}{\partial z}F(y, z)-F(y, z) ##?
  • · Replies 6 ·
Replies
6
Views
2K