Second Order Nonhomogeneous Differential Equation (Method of Undetermined
Caerswso1pc
Answered question
2022-03-31
Second Order Nonhomogeneous Differential Equation (Method of Undetermined Coefficients) Find the general solution of the following Differential equation . We know that the general solution for 2nd order Nonhomogeneous differential equations is the sum of where is the general solution of the homogeneous equation and the solution of the nonhomogeneous. Therefore . Now we have to find . I know in fact that . Now we have to find yp. I know in fact that but i do not know how to get there.
Answer & Explanation
Nunnaxf18
Beginner2022-04-01Added 18 answers
Step 1 since the RHS is a soln of the homogeneous eqn, we can try x multiplied by it. let be a linear combination of and . Step 2 Let , where D is the derivative operator. equating coeffs,
Riya Erickson
Beginner2022-04-02Added 12 answers
Step 1 After a lot of trial and error i finnaly understand the strategy behind this type of differential equation. So here's is what i did in order to find the solution (I will provide as much information as i can) In order to calculate a nonhomogeneous differntial equation we must first find the general solution of the homogeneous. So (1) using the Auxiliary equation we can easily find that the general solution is . Now as cineel mentioned above we can try multiplied by x. Thus . Now we have to differentiate two times. So (1) (2) (3) Step 2 Therefore substituting (1)(2)(3) in our original differential equation we end up with So Thus (1) Now becomes So