Question

Classify each equation as linear or nonlinear dy/dx = y^3 - 9 linear y" = 3y' - 6 nonlinear > 3y y' = 6-4 linear > 4x^2 y" - 3x y' + 4y = 2x - 4 linear

Answer 1

We know that general equation of linear differerential equation is an(x) any + Cu(a) dy + Q(x) yg = E(X) any (a) do dan y dan- da Now we chassify a all the given differential tareation below. dy y3 gy. da ay - y²+gy this equation contain y3 term So the da equation is non-linear I first order differential equation.

y"=34'-6 12y and get and y" = on da? Put y'= dy da 3dy - 6 day dx2 da this equation is linear 422 da? 3 dy =-6. da 34 y'=64-4 Put y' din dt and get 34 dy dt - 6t - 4 thus non linear equation. Since this equation contains 34 dni term. so 3yy'=62-4 non-linear differential equation. a 4x²y"-3ky't Ay=2x-4 put y = dy da and ylla 423 and get da2 3r dy da 4x² day + Ay = 2-4, ax2 compare the general equation of linear differential equation this equation satisfy all the condition this is linear, so therefore are²y" - 38 ytan =2x=4 is linear equation.