What is the order and degree of the following differential

Question

1. What is the order and degree of the following differential equation?

(a) Order 2, degree 1 (b) order 1, degree 2 (c) order 2, degree 2  (d) None of these

2. Which of the following equations are exact ?

(1) (4x+3y+1) dx + (3x+2y +1) dy = 0

(2) x(x²+3y²) dx+ y(y²+3x²) dy= 0

(3) y (2xy+ e^x) d^x =   dy

(4) x²y dx - ( x³- y³) dy =0

(a) 1,2,4 (b) 1,2  (c) 2,3,4 (d) all of these

3. What is the value of the constant λ such that ( 2xe^y + 3y²)dx/dy + ( 3x² + λe^y ) = 0 is exact?

(a)  λ = 2  (b) λ = 3  (c) λ=1/2 h  (d) None of these

4.  Classify the following differential equation

X² ( y+1) dx + y² ( x-1) dy=0

(a)  Linear but not separable

(b) Separable but not linear

(c) Neither separable nor linear

(d) None of these

5. What is the integrating factor of the following differential equation

Y(x²y²+2 ) dx + x( 2- 2x²y²) dy = 0

(a) 1/x³y³     (b)  3x²y²  (c)1/3x³y³  (d) None of these

6.  Describe the type of the following differential equation

P³ - p(y+3) +x = 0

(a) Solvable for p (b) solvable for x (c) solvable for y (d) None of these

7. What is the general solution of the following differential equation

Sin px cos y = cos px sin y + p

(a)  Y= cx + sin c (b) y = cx + sin^-1 c (c) y = cx - sin-1c (d) None of these

8. What is the wronskian of  e^x, e^-x, cosh x ?

(a)e^x  (b) e^-x  (c) 0 (d) None of these

Attachment:- Questions of differential equation.pdf