Advanced Engineering Mathematics, 2 Sub edition

Book Preface

Introduction to Differential Equations

1. Second-order; linear.
2. Third-order; nonlinear because of (dy/dx)4.
3. The differential equation is first-order. Writing it in the form x(dy/dx) + y2 = 1, we see that it is nonlinear in
y because of y2. However, writing it in the form (y2 − 1)(dx/dy) + x = 0, we see that it is linear in x.
4. The differential equation is first-order. Writing it in the form u(dv/du)+(1+ u)v = ueu we see that it is linear
in v. However, writing it in the form (v + uv − ueu)(du/dv) + u = 0, we see that it is nonlinear in u.
5. Fourth-order; linear
6. Second-order; nonlinear because of cos(r + u)
7. Second-order; nonlinear because of

1 + (dy/dx)2
8. Second-order; nonlinear because of 1/R2
9. Third-order; linear
10. Second-order; nonlinear because of xË™ 2………………………………..