Differential Equations – 1 – 1

1. The solution of a differential equation which is not obtained from the general solution is known as :

(a) Particular solution
(b) Singular solution
(c) Complete solution
(d ) Auxiliary solution

2. The differential equation dy/dx = y² is :

(a) Linear
(b) Non-linear
(c) Quasilinear
(d ) None of these

3. The differential equation formed by y= acosx + bsinx + 4 where a and b are arbitrary constants is :

(a) (d²y/dx²) + y = 0
(b) (d²y/dx²) – y = 0
(c) (d²y/dx²) + y = 4
(d) (d²y/dx²) – y = 4

4. The general solution of (x² D² – xD), y= 0 is :

(a) y = C₁ + C₂ e^x
(b) y = C₁ + C₂ x
(c) y = C₁ + C₂ x²
(d) y = C₁ x + C₂ x²

5. The equation a₀ x²y″+ a₁xy′+ a₂y = φ(x) is called :

(a) Legendre’s linear equation
(b) Cauchy’s linear equation
(c) Simultaneous equation
(d) Method of undetermined coefficients

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