Question

3. a) Classify each ODE by order and linearity: y" – 3xy' + xy = 0 b) y(4) + 2xy" - x?y' - xy' + sin y = 0 c) 2.5** 12.5x = sint

Answer 1

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© consider, %) 1 2 3 4"- x^2-x) - soc 0 —- I Here Highet oseler derivative in differential equation Ils on y(4) which and has order 4 e Order of given differential equation is 4 H. Also, given. Differential equation is not in form I of equation ( siny Po present in @ & siny is not con Tunction of x) I giver differential equation is none linear. g19) tamy 1"-2²ylaxy of siny =0 is 4th oseler non-linears ordinary differential equation. Prin consider, (2015) algo + 12052 = sint. - ? dea here è is highest orden derivative present in e at? ealer of ③ is 2 Also given differential ear iseen the form of the form pcH de of actix & ret) flineer form) given differential equation is linear dL4 6.5) dx of (125) x = sint is an an order linear dt cocinamy differential equation,

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