Practice question · Fill in the blanks
Complete the following passage by choosing the correct terms from the word bank.
The general solution of a nonhomogeneous ODE is _h + , where is the ______ solution and y_p is a ______ solution.
Word bank: homogeneous · particular · general · singular
Hints
- The general solution has two parts with different jobs.
- One part solves the equation with the forcing removed.
Show the answer
The general solution of a nonhomogeneous ODE is _h + , where is the homogeneous solution and y_p is a particular solution.
Why
y_h solves the associated homogeneous equation; y_p satisfies the full equation.
Practise Problem-Solving: Differential Equations
The app has 6 more questions on this lesson, and keeps your place in the course. Physics I is free to start.
More questions on Problem-Solving: Differential Equations
- Sort each ODE by the best solution strategy.
- An RLC circuit is switched on and rings toward steady state. Order the analysis a physicist performs.
- Choosing between separation of variables, integrating factors and Laplace transforms is usually decided…
- The superposition principle applies to all linear differential equations, homogeneous and nonhomogeneous…
- Which methods can solve a first-order linear ODE?