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Lchan1
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oh. e... hahahaa thanks
Can u=y/x be used to solve x(dy/dx)=y+e^(8x/y)?
- Thread starter Lchan1
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SUMMARY
The discussion centers around solving the differential equation x(dy/dx) = y + e^(8y/x). Participants emphasize the importance of the substitution u = y/x to simplify the equation. The correct approach involves using the quotient rule and chain rule for derivatives, leading to the expression for dy/dx in terms of u and x. Ultimately, the solution is derived as y = ln(ln(1/x^8))(x)/-8, with the domain restriction that x cannot be zero.
PREREQUISITES- Understanding of differential equations and their solutions
- Familiarity with the quotient rule and chain rule in calculus
- Knowledge of exponential functions and logarithms
- Ability to perform variable substitution in differential equations
- Study the application of the quotient rule in solving differential equations
- Learn about variable substitution techniques in differential equations
- Explore the properties of logarithmic and exponential functions
- Practice solving similar differential equations using substitution methods
Students studying calculus, particularly those focusing on differential equations, as well as educators seeking to clarify concepts related to variable substitution and derivative rules.
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