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

Question

chihiroasleaf · Answer

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..

anonymous · Answer

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

klimenkov · Answer

What is that 1 in the second addend?

amistre64 · Answer

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

amistre64 · Answer

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

anonymous · Answer

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

amistre64 · Answer

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

amistre64 · Answer

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