Example (1)y+2y=0;(ODE) (2)xy”+y=x2:(ODE) (3)y"-x6y3+y=0: 4日10y4至，1无2000 Peipei Shang School of Mathematical Sciences shang@tongji.edu.Ordinary Differential Equations
Example (1) y 0 +2xy = 0; (ODE) (2) xy00 +y 0 = x 2 ; (ODE) (3) y 000 −x(y 0 ) 3 +y = 0; (ODE) (4) d 2 y dt 2 +y = cos 2t; (ODE) (5) ∂ 2T ∂ x 2 + ∂ 2T ∂ y 2 + ∂ 2T ∂ z 2 = 0; (PDE) (6) ∂ 2u ∂ x 2 = ∂u ∂ t +u. (PDE) Remark There are multiple criteria to classify ODEs. Peipei Shang School of Mathematical Sciences shang@tongji.edu.cn Ordinary Differential Equations
Example (1)y+2y=0;(ODE) (2)9y"+y=x2;(ODE) (3)y"-xy)3+y=0;(ODE) 4日10y4至，1无2000 Peipei Shang School of Mathematical Sciences shang tongji.edu.Ordinary Differential Equations
Example (1) y 0 +2xy = 0; (ODE) (2) xy00 +y 0 = x 2 ; (ODE) (3) y 000 −x(y 0 ) 3 +y = 0; (ODE) (4) d 2 y dt 2 +y = cos 2t; (ODE) (5) ∂ 2T ∂ x 2 + ∂ 2T ∂ y 2 + ∂ 2T ∂ z 2 = 0; (PDE) (6) ∂ 2u ∂ x 2 = ∂u ∂ t +u. (PDE) Remark There are multiple criteria to classify ODEs. Peipei Shang School of Mathematical Sciences shang@tongji.edu.cn Ordinary Differential Equations
Example (1)y+2y=0;(ODE) (2)9y"+y=x2;(0DE) (3)y"-xy)3+y=0:(ODE) (4) $+y=c0s2, 4日10y至，1元3000 Peipei Shang School of Mathematical Sciences shang tongji.edu.Ordinary Differential Equations
Example (1) y 0 +2xy = 0; (ODE) (2) xy00 +y 0 = x 2 ; (ODE) (3) y 000 −x(y 0 ) 3 +y = 0; (ODE) (4) d 2 y dt2 +y = cos 2t; (ODE) (5) ∂ 2T ∂ x 2 + ∂ 2T ∂ y 2 + ∂ 2T ∂ z 2 = 0; (PDE) (6) ∂ 2u ∂ x 2 = ∂u ∂ t +u. (PDE) Remark There are multiple criteria to classify ODEs. Peipei Shang School of Mathematical Sciences shang@tongji.edu.cn Ordinary Differential Equations
Example (1)y+2y=0;(ODE) (2)9y"+y=x2;(ODE) (3)y"-xy3+y=0:(ODE) (4) g象+y=cos2,(ODE) 4日10y至，1元3000 Peipei Shang School of Mathematical Sciences shang tongji.edu.Ordinary Differential Equations
Example (1) y 0 +2xy = 0; (ODE) (2) xy00 +y 0 = x 2 ; (ODE) (3) y 000 −x(y 0 ) 3 +y = 0; (ODE) (4) d 2 y dt2 +y = cos 2t; (ODE) (5) ∂ 2T ∂ x 2 + ∂ 2T ∂ y 2 + ∂ 2T ∂ z 2 = 0; (PDE) (6) ∂ 2u ∂ x 2 = ∂u ∂ t +u. (PDE) Remark There are multiple criteria to classify ODEs. Peipei Shang School of Mathematical Sciences shang@tongji.edu.cn Ordinary Differential Equations
Example (1)y+2y=0;(ODE) (2)y”+y=x2;(OD) (3)y"-x6y3+y=0:(ODE) (4)朵+y=cos2;(0DE) (5) 骆++昭=0， 4日10y至，1元3000 Peipei Shang School of Mathematical Sciences shang tongji.edu.Ordinary Differential Equations
Example (1) y 0 +2xy = 0; (ODE) (2) xy00 +y 0 = x 2 ; (ODE) (3) y 000 −x(y 0 ) 3 +y = 0; (ODE) (4) d 2 y dt2 +y = cos 2t; (ODE) (5) ∂ 2T ∂ x 2 + ∂ 2T ∂ y 2 + ∂ 2T ∂ z 2 = 0; (PDE) (6) ∂ 2u ∂ x 2 = ∂u ∂ t +u. (PDE) Remark There are multiple criteria to classify ODEs. Peipei Shang School of Mathematical Sciences shang@tongji.edu.cn Ordinary Differential Equations