Differential Equations Answers

For second order phase transitions, show that
Δp/ΔT ={(Cp2–Cp1)/(Tv(αp2–αp1))}
Plot temperature variation of heat capacity for second order phase transition. How does this plot is different from the plot of lambda transitions.

: y^2 + x^2 (dy/dx)^2 -2xy (dy/dx) = 4 (dx/dy)^2

Solve : y^2 + x^2 (dy/dx)^2 -2xy (dy/dx) = 4 (dx/dy)^2

1. Show that if z is abse nt from the e quation F (x, y, z, p, q)= 0,Charpit's
method coincides with Jacobi's method.

2. how how to solve, by Jacobi's method, a partial differential equation of
the type f( x, delu/delx, delu/delz ) = g(y, delu/dely, delu/delz )

Solve the following ordinary differential equation.

=> d^2y/dx^2 + dy/dx + y = 0 .

State, giving reasons, whether the following statements are True or False:
(i) When a comb is run in dry hair, the comb is charged by +7e and the hair by –5e

Interpret the initial value problem d^2θ/dt^2+ß^2 θ=0, θ(0)=θ° ,dθ/dt] at (t=0) =ω°
for any physical situation and hence solve the problem

Solve the differential equation x^3 p^2 +x^2 yp+a^3=0 and also obtain its singular solution, if
it exists.

xdy/dx–y=e^(dy/dx)

d^2y/dx^2–cotxdy/dx–sinx^2 y=cosx–cos^3x