CS403 Highlighted Handouts Set 2

MTH401 (lec 9 to 15) · Quiz 1 Fall 2022 · Junaid+handouts merged · ORANGE MONKEY TEAM

1. The two function u(v) and v(y) are linearly independent if wronskian W(u,v) is________.

Equal to zero…..not sure · 2. The wronskian of two functions f(x) and g(x) is · F(x)g^’(x)-f^’(x)g(x)…..not sure

3. If an(x)=0 in the differential equation an(x)dny/dxn+an-1dn-1/dxn- 1+…..+a1(x)dy/dx+a0(x)y=g(x) for some x<1 then solution of initial value problem may not be __________.

unique · 4. If wronskian W(h,z)(x)=0 then · h(x)andz(x) are linearly independent

5. If we substitute u = y/x in differential equation xdy/dx-y=x3/y(ey/x) then the given differential equation can be simplified to

ueudu=dy

6. When the arbitrary constant of the general solution of a differential equation takes some unique value, then the solution becomes the ____ of the equation

Particular solution

7. Subject to the condition y(4)=1/8 and y’(4) = - 3/64 is known as _____.

A and b both

8. In the population growth model the solution of the differential equation is given by

A(t)=A0ekt

9. In the logestic equation 1dP/pdt = a-bp the term –bp2 can be interpreted as_________.

Inhibition term…….confirm

10. In exponential growth for population growth N(t) = Noemt if m<0 then lim N(t) =

11. The other name of Verhulst pearl is

Logistic model……confirm

12. A function satisfying the differential equation on the some interval I , containing a and b , whose graph passes through two points(a, y0) and (b,y1) is called solution of the ______________ value problem .

Boundary…..confirm

13. A function satisfying the differential equation on the interval 1 whose graph passes through (x0,y0) such that the slope of the curve at the point is the number y’0 is called solution of the ________ value problem

Initial ….confirm

14. Suppose that y1, y2…..yn are n solutions of the homogeneous nth order differential equation. Then the solution is linearly dependent on an interval if and only if ____________.

W(y1,y2…..yn) ≠ 0…..confirm

15. The differential equation 4x2 (d2y/dx2 )+ 12x(dy/dx)+3y=0 subject to the condition y(4) = 1/8 and y’(4) = -3/64 is known as ________.

A & b both

16. IF X is the remaining amount of the substance A at any time t then dX/dt = KX, where K<0 because X is _________.

Decreasing…..confirm · 17. The differential equation y(1+2xy)dx+x(1-2xy)dy=0 is · Separable…..confirm

18. Wronskian W(1,ex) is ___________.
19. If A(t) is the amount of a radioactive substance present at time t, the rate of change of A(t) with respect to t is given by