MTH401 GRAND QUIZ SOLVED FILE 3|| 100% VERIFIED|| VURANK

MTH401 GRAND QUIZ SOLVED 100% VERIFIED BY ADMIN (MID TERM SYLLABUS)

Q1: If y= c₁e^{(-2 + √6)x} + c₂e^{(-2 - √6)x} is the complementary solution of:

A) Ax + B

D) Ax² + Bx + C

D) Ax³ + Bx² + Cx + D (Confirm) (100% Sure)

D) (Ax² + Bx)2x²

Q2: If initial amount of radioactive isotope is 100g. What will be the amount at the end of 30 days such that K=0.043?

A) 371.415

B) 380.560

B) 363.297 (Confirm Solved) (100% Sure)

B) 360.351

Q3: If 2,3,5 are real roots of a differential equation, then the general solution is ________.

A) y_c = c₁e^2x + c₂e^3x + c₃e^5x (confirm Solved) (100% Sure)

B) y_c = c₁e^2x + c₂e^-3x + c₃e^5x

B) y_c = c₁e^2x + c₁e^-3x + c₁e^5x

B) y_c = (c_{1 + c2 + c3)e^3x+ e^2x}

Q4: Wronskian W(x,2x) = __________.

A) 0 (Confirm Solved) (100% Sure)

B) 1

B) -1

B) None of these

Q5: Which of the following is the implicit solution of the differential equation: ^dy⁄_dx = - ^x⁄_y ,

A) x + y + 4 =0

B) x² + y² - 4 =0 (page16) (100% Sure)

B) x² - y² + 4 =0

B) x² - y² - 4 =0

Q6: ydx - y(sinx)dy = 0, is an example of ______ differential equation.

A) Exact (page33) (100% Sure)

B) Non-exact

B) Non-linear

B) Non-homogeneous

Q7: Which of the following is an example of ordinary differential equation?

A) (y - x)dx + 4xdy = 0 (page15) (100% Sure)

B) ∂u ⁄ ∂y = - ∂u ⁄ ∂x

B) ax² + bx + c = 0, a≠0

B) ɸ(x) = f(x) + ƛ ∫ k(x,t) ɸ(t)dt

Q8: A differential equation M(x,y)dx + N(x,y)dy = 0 is exact if there exists a multi-variable function f(x,y) such that _______.

A) df(x,y) = ∂f ⁄ ∂x dx + ∂f ⁄ ∂y dy (100% Sure) Click here for Reference

B) ∫ f(x,y)dx = ∫ ∂f ⁄ ∂x dx + ∫ ∂f ⁄ ∂y dy

B) f(x,y) = ∂f ⁄ ∂x dx + ∂f ⁄ ∂y dy

B) f(x,y) = ∫ ∂f ⁄ ∂x dx + ∫ ∂f ⁄ ∂y dy

Q9: Which of the following is an initial value problem (IVP)?

A) d²y ⁄ dx² + y = 0

B) d²y ⁄ dx² + y = 0, x ⋴ |-2, 2|

B) d²y ⁄ dx² + y = 0, y(1) = -2 and y'(1)= -2 (Confirm Solved) (100% Sure)

B) d²y ⁄ dx² + y = 0, y(1) = -2 and y'(^Π ⁄ ₂)= -2

Q10: Which of the following would be a constant solution of the separable differential equation: ^dy ⁄ _dx = e^x+y ?

A) y = 0 (Confirm Solved) (100% Sure)

B) y = 1

B) y = a ⋴ R

B) No constant solution exist