Differential Equations Answers

b) Find the solution of the Riccati equation

dy/dx=(2cos^2x-sin^2x+y^2)/2cosx ;y(x)=sinx

Find the value of b for which the equation

(1 )( ye^2xy + x )dx + bxe^2xy dy = 0

is exact, and hence solve it for that value of b

State whether the following statements are true or false. Justify yourself with the help of

a short proof or a counter example(1)Equation x^2 ( y − px) = yp^2 is reducible to clairaut’s form

State whether the following statements are true or false. Justify yourself with the help of

a short proof or a counter example(1).y = 0, is a singular solution of the differential equation 27y-8(dy/dx)^3=0

State whether the following statements are true or false. Justify yourself with the help of

a short proof or a counter example.

i) y'+ P(x) y = Q(x) y^2 is a linear equation for integral values of n.

State whether the following statements are true or false. Give reasons for your answers (2) The function f(x, y) =max{y/x, x} is a homogenous function on R^2

Given that z = ax + √a² − 4y + c 2 is the complete integral of the PDE, p² − q² =4 determine its general integral.

A wet porus substance in the open air loses its moisture at a rate proportional to the

moisture content, if a sheet hung in the wind loses half its moisture during the first

hour, then find the time when it has lost 95% moisture provided the weather

conditions remain the same.

State whether the following statements are true or false. Justify yourself with the help of a short proof or a counter example. (3) dz/dx.dz/dy-(dz/dy) ^2=0is a non -linear PDE.

State whether the following statements are true or false. Justify yourself with the help of a short proof or a counter example. (2) The solution of PDE dz/dx+dz/dy=z^2 is z=-[y+f(x-y) ].