Question

Consider the ODE y' + P(x)y = f(x). If P(x) and f(x) are both constants, then the ODE can be solved by the separation of variables. Suppose P(x) = a and f(x) = b, where a and b are non-zero constants. We then have the ODE y' + ay = b. If y(0) = C₀. Verify by substitution that the explicit solution satisfies the ODE.

Name: consider the ode y pxy fx if px and fx are both constants then the ode can be solved by the separation of variables suppose px a and fx b where a and b are non zero constants we then have th 20235
Uploaded: 2023-04-09T18:10:36-08:00
Duration: 3 min 29 s
Channel: Sam Stansfield
Description: consider the ode y pxy fx if px and fx are both constants then the ode can be solved by the separation of variables suppose px a and fx b where a and b are non zero constants we then have th 20235

          Consider the ODE y' + P(x)y = f(x). If P(x) and f(x) are both constants, then the ODE can be solved by the separation of variables. Suppose P(x) = a and f(x) = b, where a and b are non-zero constants. We then have the ODE y' + ay = b. If y(0) = C₀. Verify by substitution that the explicit solution satisfies the ODE.

Added by John O.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Sam Stansfield

04/09/2023

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Consider the ODE y' + P(x)y = f(x). If P(x) and f(x) are both constants, then the ODE can be solved by the separation of variables. Suppose P(x) = a and f(x) = b, where a and b are non-zero constants. We then have the ODE y' + ay = b. If y(0) = C₀. Verify by substitution that the explicit solution satisfies the ODE.