General Solution for dy/dt=2ty+4e^(t^2)

Click For Summary
SUMMARY

The general solution for the differential equation dy/dt = 2ty + 4e^(t^2) is confirmed to be y(t) = e^(t^2)(4t + k), where k is a constant. This solution can be verified by substituting y(t) and its derivative dy/dt back into the original equation, which should yield a result of 0. The discussion emphasizes the correctness of the solution and the method of verification.

PREREQUISITES
  • Understanding of first-order differential equations
  • Familiarity with the method of integrating factors
  • Knowledge of exponential functions and their derivatives
  • Ability to perform substitution in differential equations
NEXT STEPS
  • Study the method of integrating factors for solving differential equations
  • Learn about verifying solutions to differential equations through substitution
  • Explore the properties of exponential functions in differential equations
  • Investigate more complex differential equations and their general solutions
USEFUL FOR

Students and professionals in mathematics, particularly those focusing on differential equations, as well as educators looking for clear examples of solution verification methods.

stasianlov
Messages
1
Reaction score
0
find general solution for differential equation dy/dt=2ty+4e^(t^2)

i got e^(t^2)(4t+k) is that right?
 
Physics news on Phys.org
hi stasianlov! :smile:

(try using the X2 button just above the Reply box :wink:)
stasianlov said:
find general solution for differential equation dy/dt=2ty+4e^(t^2)

i got e^(t^2)(4t+k) is that right?

yes that's fine :smile:

what is worrying you about that? :confused:​
 
you can check the answer by substituting the solution y(t) and its derivative dy/dt in the differential equation. The results should be 0.
 

Similar threads

MHB 2.1.7 DE y'e -2ty =2te^(-t^2)
  • · Replies 3 ·
Replies
3
Views
2K
Graduate General Solution of dy/dt = -2ty + 4e^(-t^2) w/ Initial Value Problem
  • · Replies 1 ·
Replies
1
Views
3K
MHB Help with a question (Bernoulli General solution)
  • · Replies 8 ·
Replies
8
Views
3K
MHB -1.3.14 Verify the following given functions is a solution
  • · Replies 7 ·
Replies
7
Views
2K
Undergrad Question about solving linear first order non-homogeneous ODEs
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad General solution of heat equation?
  • · Replies 3 ·
Replies
3
Views
3K
Undergrad Determining equilibrium solutions to differential equations
  • · Replies 16 ·
Replies
16
Views
4K
MHB Partial differential equations problem - finding the general solution
  • · Replies 2 ·
Replies
2
Views
2K
Graduate Equations with dependent variable missing
  • · Replies 3 ·
Replies
3
Views
2K
MHB -find general solution y'+2y=2-e^(-4t), y(0)=1
  • · Replies 7 ·
Replies
7
Views
4K