Differential Equations Answers

4. (a)Find the general solution of the partial differential equation.

zxy =(6x^3)y


(b) Find the particular solution for which z(x,0) = 6x^2 , z(1, y) = 6cos y

A series RLC circuit with R = 6 ohm, C = 0.02 Farad and L = 0.1 has no applied voltage. Find the subsequent current in the circuit if the initial charge, on the capacitor is q0 and the initial current is zero.

Solution of (D^3 -D)y = x^3 is

A series RLC circuit with R = 6 ohm, C = 0.02 Farad and L = 0.1 has no applied voltage. Find the subsequent current in the circuit if the initial charge, on the capacitor is q0 and the initial current is zero.

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^n is a linear equation for integral values of n.


ii) y = 0, is a singular solution of the differential equation 27y-8(dy/dx)^3=0


iii) Equation x^2 ( y − px) = yp^2 is reducible to clairaut’s form

Find fx(0,0) and fx (x,y) ,where (x, y) ≠(0,0) for the following function


f (x,y)={xy^3/x^2+y^2 , (x,y)not=to (0,0)

0 (x,y)= to (0,0). }



Is fx continuous at (0,0) ? Justify your answer.

A series RLC circuit with R = 6 ohm, C = 0.02 Farad and L = 0.1 has no applied voltage. Find the subsequent current in the circuit if the initial charge, on the capacitor is q0 and the initial current is zero.

Find the cylindrical coordinates of the points where the Cartesian coordinates are



i)( 6,6,8)

ii) ( √2,1,1)

Solve the differential equation :

(x^2)y'' - y' - 4(x^3)y = 8(x^3)sin(x^2)