Differential Equations Answers

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) ].

State whether the following statements are true or false. Justify yourself with the help of a short proof or a counter example. (1) Equation cos(x+y) p+sin(x+y) q=z^2+z is a quasi -linear equation.

Find the integral surface of the partial differential equation
(X-y)y^2p+(y-x)x^2q=(x^2+y^2)z

Apply method of variations of parameters to solve the following differential equations
X^2 d^2y/dx^2 +xdy/dx -y=x^2 e^x

Solve the following differential equations changing the independent variables
X^2 d^2y/dx^2 - dy/dx - 4x^3 y= 8x^3 sinx^2 ,X>0.

Solve differential equations dy/dx=1+(dy/dx)^2.

(Xy^2 -x^2 )dx + ( 3x^2 y^2 + x^2 y-2x^3 + y^2) dy =0