Engineering Board Exam Reviewer · Nonhomogeneous Second-Order Equations · hard

Use variation of parameters to solve y''+y= x for 0<x< π2.

1. y = C1 x + C2 x + x x - ≤ft( x ) x
2. y = C1 x + C2 x + x x + ≤ft( x ) x
3. y = C1 x + C2 x - x x + ≤ft( x ) x
4. y = C1 x + C2 x + x x + ≤ft( x ) x

Answer

B. y = C1 x + C2 x + x x + ≤ft( x ) x

Solution

y1= x, y2= x, W=1. Then u1'=-y2 x/W=- x u1= ( x) and u2'=y1 x/W=1 u2=x. So yp= x ( x)+x x and y=C1 x+C2 x+ x ( x)+x x.

More Nonhomogeneous Second-Order Equations questions

1. Find the general solution of y''-4y'+4y=e2x.
2. Find the general solution of y''+y= x.
3. Solve y''+y=2 with y(0)=0 and y'(0)=0, and find y(π).
4. Find the general solution of y''+3y'+2y=12x2.
5. Find the general solution of y''-2y'-3y=6e-x.
6. Find the general solution of y''+4y=8e2x.
7. Find the general solution of y''-3y'+2y=4x.
8. Find the general solution of y''+y'-2y=6.
9. Find the general solution of y''-y=4.

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