Solve Nonlinear First Order Differential Equation | y'(t)=y(t)^3+f(t)

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SUMMARY

The discussion focuses on solving the nonlinear first-order differential equation y'(t) = y(t)^3 + f(t). A suggested method for finding y(t) involves substituting z = 1/y^2, which simplifies the equation under certain conditions. The approach emphasizes the importance of variable separation and neglecting constants when the magnitude of z is large. This method is particularly relevant for those grappling with nonlinear differential equations.

PREREQUISITES
  • Understanding of first-order differential equations
  • Familiarity with nonlinear dynamics
  • Knowledge of variable substitution techniques
  • Basic calculus concepts, including differentiation
NEXT STEPS
  • Research variable separation methods in differential equations
  • Explore the implications of substituting z = 1/y^2 in nonlinear equations
  • Study examples of nonlinear first-order differential equations
  • Learn about the behavior of solutions to nonlinear differential equations
USEFUL FOR

Mathematics students, researchers in applied mathematics, and anyone interested in solving nonlinear differential equations will benefit from this discussion.

bpcraig
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Maybe I'm just dumb...

<br /> y&#039;(t)=y(t)^3+f(t)<br />

find y(t)

Thanks...
 
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bpcraig said:
Maybe I'm just dumb...

<br /> y&#039;(t)=y(t)^3+f(t)<br />

find y(t)

Thanks...
Welcome bpcrai.
Try substituting z =1/y^2 if permissible. If the magnitude of z is large in the range, we can neglect a constant & separate the variables.

P.S. : I'm afraid everybody's dumb at solving nonlinear differential equations. ;)
 

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