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ASAAD123

  • 3 years ago

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

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  1. chihiroasleaf
    • 3 years ago
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    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..

  2. ASAAD123
    • 3 years ago
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    \[x''-(1\frac{ x'^2 }{ 3 })x'+x=0\] linear or nonlinear?

  3. klimenkov
    • 3 years ago
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    What is that 1 in the second addend?

  4. amistre64
    • 3 years ago
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    if the highest power of a derivative is 1, its linear. y' = y+2 is linear (y')^3 = y+2 ..... is not linear

  5. amistre64
    • 3 years ago
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    the largest number of ''''s defines order the power of a derivative defines the degree .... a degree of 1 is linear

  6. ASAAD123
    • 3 years ago
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    for example, \[\frac{ d^2y }{dx^2 }+(\frac{ 1-x }{ 2-sinx })\frac{ dy }{ dx }+2y=siny\] ,is it linear or not linear and why? @amistre64

  7. amistre64
    • 3 years ago
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    the degree is 1, so its linear the order is 2, since there is a 2nd derivative in there

  8. amistre64
    • 3 years ago
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    \[\left(\frac{ d^2y }{dx^2 }\right)^1+(\frac{ 1-x }{ 2-sinx })\left(\frac{ dy }{ dx }\right)^1+2y=siny\]

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