- #1
mistereko
- 25
- 0
Homework Statement
How do I get y'' - yω2 = y'(sinωx + sinhωx) + y(cosωx*ω + coshωx*ω)
equal to
y'' - yω2 = sinωx + sinhωx
I'm baffled.
Solving Funny Trig Equation y'' - yω2 = sinωx + sinhωx
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SUMMARY
The discussion centers on the differential equation y'' - yω² = y'(sinωx + sinhωx) + y(cosωx*ω + coshωx*ω). Participants express confusion regarding the simplification of this equation to y'' - yω² = sinωx + sinhωx. The consensus is that the right-hand side resembles the differentiation of a product of two functions, indicating that direct equality may not be achievable without further manipulation or specific conditions.
PREREQUISITES- Understanding of second-order differential equations
- Familiarity with trigonometric and hyperbolic functions
- Knowledge of product differentiation rules
- Basic skills in mathematical manipulation and simplification
- Study the method of solving second-order linear differential equations
- Learn about the application of the product rule in calculus
- Research techniques for simplifying complex differential equations
- Explore the properties of trigonometric and hyperbolic functions in differential equations
Students studying differential equations, mathematicians tackling complex equations, and educators seeking to clarify concepts related to trigonometric and hyperbolic functions in mathematical contexts.
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