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in Differential Equations,how to know that Equation is linear or nonlinear?
 one year ago
 one year ago
in Differential Equations,how to know that Equation is linear or nonlinear?
 one year ago
 one year ago

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chihiroasleafBest ResponseYou've already chosen the best response.0
check whether \(L(u+v) = L(u) + L(v) \) and \(L(cu) = c L(u) \) L is operator... if the equation satisfy both of these, then it's linear..
 one year ago

ASAAD123Best ResponseYou've already chosen the best response.0
\[x''(1\frac{ x'^2 }{ 3 })x'+x=0\] linear or nonlinear?
 one year ago

klimenkovBest ResponseYou've already chosen the best response.0
What is that 1 in the second addend?
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
if the highest power of a derivative is 1, its linear. y' = y+2 is linear (y')^3 = y+2 ..... is not linear
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
the largest number of ''''s defines order the power of a derivative defines the degree .... a degree of 1 is linear
 one year ago

ASAAD123Best ResponseYou've already chosen the best response.0
for example, \[\frac{ d^2y }{dx^2 }+(\frac{ 1x }{ 2sinx })\frac{ dy }{ dx }+2y=siny\] ,is it linear or not linear and why? @amistre64
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
the degree is 1, so its linear the order is 2, since there is a 2nd derivative in there
 one year ago

amistre64Best ResponseYou've already chosen the best response.0
\[\left(\frac{ d^2y }{dx^2 }\right)^1+(\frac{ 1x }{ 2sinx })\left(\frac{ dy }{ dx }\right)^1+2y=siny\]
 one year ago
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