-1²/2 Find the general solution of x"+x'+x=0 given that x= e¯ is one solution. Show that x1(t) = t is a solution of the equation x"—tx'+x=0. Use reduction of order to find a second solution x2(t). One solution of x "- t+2 =x²+²=-2²-² -x=0 is x₁(t)=t. Find a second independent solution. t+2

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
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use reduction of order

 

1) Find the general solution of x"+x²+x=0 given that x = e-²/2 is one solution.
2) Show that x1(t) = t is a solution of the equation x"-tx'+x=0. Use reduction of order to find a second solution x2(t).
5) One solution of x "-
t+2
t + 2
-x'+
t
t"
- x = 0 is x₁₂ (t) =
)= t. Find a second independent solution.
Transcribed Image Text:1) Find the general solution of x"+x²+x=0 given that x = e-²/2 is one solution. 2) Show that x1(t) = t is a solution of the equation x"-tx'+x=0. Use reduction of order to find a second solution x2(t). 5) One solution of x "- t+2 t + 2 -x'+ t t" - x = 0 is x₁₂ (t) = )= t. Find a second independent solution.
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