Solve : y 2 r – 2ys + t = p + 6y.
Answers
Answer:
9.1 Introduction
The most general form of a partial differential equation of
order two with dependent variable z and two independent variables x
and y is expressed as
f ( x , y ,z, p , q,r,s,t )=0 …(1)
where p≡
∂ z
∂ x
, q≡
∂ z
∂ y
, r ≡
∂
2
z
∂ x
2
, s≡
∂
2
z
∂ x ∂ y
and t≡
∂
2
z
∂ y
2
…
(2)
If any one or more of the partial derivatives r, s, t appear in
more than one degree in (1), then it is called a non-linear partial
differential equation of order two.
Sometimes equation (1) can be put in the form
Rr+Sr+Tt +Pp+Qq+Zz=F …(3)
where the coefficients R, S, T, P, Q, Z and F are not all zero or
constants, but are the variable coefficients.
The partial differential equations of the form (3) may be
classified as quasi-linear, semi-linear and linear as follows: