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Solve the initial-value linear first order Differential Equation (ODE) problem. State the largest interval I, on which the solution is defined (x + 1) + y = ln(x), y(1) = 10 dx This ODE will produce and explicit solution. Solve the above problem through the following steps: 1. Place the linear ODE in its standard form. 2. Calculate the integration factor. 3. Multiply the standard form of the equation by the integration factor. 4. LHS of the resulting equation produced in point 3 above, is the derivative of the integrating factor and y. 5. Integrate both sides of the resulting equation produced in point 4 above (Hint: RHS - use integration by parts). 6. Write down the solution of ODE. 7. Apply initial condition (IC) to the solution above and solve for constant "C". 8. Write down the final solution of the ODE and state the solution interval.

Solve the initial-value linear first order Differential Equation (ODE) problem. State the largest interval I, on which the solution is defined (x + 1) + y = ln(x), y(1) = 10 dx This ODE will produce and explicit solution. Solve the above problem through the following steps: 1. Place the linear ODE in its standard form. 2. Calculate the integration factor. 3. Multiply the standard form of the equation by the integration factor. 4. LHS of the resulting equation produced in point 3 above, is the derivative of the integrating factor and y. 5. Integrate both sides of the resulting equation produced in point 4 above (Hint: RHS - use integration by parts). 6. Write down the solution of ODE. 7. Apply initial condition (IC) to the solution above and solve for constant "C". 8. Write down the final solution of the ODE and state the solution interval.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter11: Differential Equations
Section11.CR: Chapter 11 Review
Problem 33CR
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Solve the initial-value linear first order Differential Equation (ODE) problem. State the largest interval I, on which the solution is defined (x + 1) + y = ln(x), y(1) = 10 dx This ODE will produce and explicit solution. Solve the above problem through the following steps: 1. Place the linear ODE in its standard form. 2. Calculate the integration factor. 3. Multiply the standard form of the equation by the integration factor. 4. LHS of the resulting equation produced in point 3 above, is the derivative of the integrating factor and y. Integrate both sides of the resulting equation produced in point 4 above (Hint: RHS - use integration by parts). 5. 6. Write down the solution of ODE. 7. Apply initial condition (IC) to the solution above and solve for constant "C". 8. Write down the final solution of the ODE and state the solution interval.
Transcribed Image Text:Solve the initial-value linear first order Differential Equation (ODE) problem. State the largest interval I, on which the solution is defined (x + 1) + y = ln(x), y(1) = 10 dx This ODE will produce and explicit solution. Solve the above problem through the following steps: 1. Place the linear ODE in its standard form. 2. Calculate the integration factor. 3. Multiply the standard form of the equation by the integration factor. 4. LHS of the resulting equation produced in point 3 above, is the derivative of the integrating factor and y. Integrate both sides of the resulting equation produced in point 4 above (Hint: RHS - use integration by parts). 5. 6. Write down the solution of ODE. 7. Apply initial condition (IC) to the solution above and solve for constant "C". 8. Write down the final solution of the ODE and state the solution interval.
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