# Find the general solutions to the given differential equations:y(6)+y"=0y(3)+3y"+3y'+y=0

Question
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Find the general solutions to the given differential equations:

• y(6)+y"=0
• y(3)+3y"+3y'+y=0
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Step 1

The differential equations are given by,

Step 2

Obtain the characteristic equation. help_outlineImage Transcriptionclose(6) The characteristic equation of the differential equation y y" 0 is mo m n2 = 0 6 Solve the equation m° + m' m2 (m2 +1)0 m 0 or m* 1 0 0 or m m fullscreen
Step 3

Solve the equation m 4&... help_outlineImage Transcriptionclosem2 и? 3 -1 Assume m? 3Dи] и %3Dti и 3і or u %3 -i m2 ior m2 = - (x+iy)iSubstitute m xiy (x+byi x* - у +12ху —і or x*- y* + i2xy%3D-i х? - у? +12ху — і%3D0 or x* - y? +i2ку +і-0 i or х fullscreen

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