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# 5_HW - y-2 xy 2 y = 0 find a second linearly independent...

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Math 2233 Homework Set 5 1 Determine whether the given equation is linear or nonlinear. If it is linear, write it in standard form and state whether it is homogeneous or non-homogeneous. (a) xy +2 x 3 y + y =0 (b) y + xy + y 2 =2 x (c) 3 y +2 y + y = x 5 2. Verify that the two given functions are linearly independent solutions of the given homogeneous equation and then find the general solution. (a) y +9 y =0 , y 1 ( x ) = sin(3 x ), y 2 ( x ) = cos(3 x ) (b) y +2 y - 15 y =0 , y 1 ( x )= e 3 x , y 2 ( x )= e - 5 x (c) y +4 y +4 y =0, y 1 ( x )= e - 2 x , y 2 ( x )= xe - 2 x 3. Given that y 1 ( x )= e 3 x is one solution of y - 5 y +6 y = 0, find a second linearly independent solution and then write down the general solution. 4. Given that y 1 ( x )= e 2 x is one solution of y - 4 y = 0, find a second linearly independent solution and then write down the general solution. 5. Given that y 1 ( x )=
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Unformatted text preview: y-2 xy + 2 y = 0, find a second linearly independent solution and then write down the general solution. 6. Given that y 1 ( x ) = x sin( x ) is one solution of x 2 y-2 xy + ( x 2 + 2) y = 0, find a second linearly independent solution and then write down the general solution. 7. Find the general solution of the following differential equations (a) y-5 y = 0 . (b) y-3 y + 2 y = 0 (c) y-y-20 y = 0 (d) y-13 y + 42 y = 0 (e) y + y + 7 y = 0 (f) y + 2 y + 5 y = 0 8. Solve the following initial value problems. (a) y-9 y = 0, y (0) = 1, y (0) = 2 . (b) y-2 y + y = 0, y (0) = 2, y (0) = 1 . (c) y + 2 y + 2 y = 0 , y (0) = 1, y (0) =-1 1...
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