## ASAAD123 2 years ago in Differential Equations,how to know that Equation is linear or nonlinear?

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1. chihiroasleaf

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..

$x''-(1\frac{ x'^2 }{ 3 })x'+x=0$ linear or nonlinear?

3. klimenkov

What is that 1 in the second addend?

4. amistre64

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

the largest number of ''''s defines order the power of a derivative defines the degree .... a degree of 1 is linear

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

the degree is 1, so its linear the order is 2, since there is a 2nd derivative in there

8. amistre64

$\left(\frac{ d^2y }{dx^2 }\right)^1+(\frac{ 1-x }{ 2-sinx })\left(\frac{ dy }{ dx }\right)^1+2y=siny$