Differential Equations Answers

Find the integral surface of the equation pq=z passing through C : x₀ = 0, y₀ = s, z₀ = s²

Solve the given system of differential equation

𝑫𝒙 − 𝟐𝒙 + 𝒚 = 𝟎 , 𝑫𝒚 − 𝒙 = 0

Q2. (c) Find the general solution of the first-order linear partial differential equation xux + yuy = u and investigate first-order, quasi-linear and linear partial differential equations. 

Q2. (b)Obtain PDE z = x + ax2y2 where a, b are arbitrary constants and also analyze the partial differential equation. 

Q2. (a) For each of the following, investigate whether the partial differential equation Is linear, quasi-linear or nonlinear. If it is linear, state whether it is homogeneous or non

i) u xxx +2uxxyy + uyyy= 0

ii) . u,x +2Uxy Uyy= sin x

iii) .uxx +xuy = y 

Q2. (a) For each of the following, investigate whether the partial differential equation Is linear, quasi-linear or nonlinear. If it is linear, state whether it is homogeneous or non

i) uxxxx +2uxxyy + Uyyy= 0

ii) uxx +2uxy + uyy= sin x

iii) uxx +xuy = y 

Q2. (b) Obtain PDE z = x + ax2y2 where a, b are arbitrary constants and also analyze the partial differential equation. 

Q2. (c) Find the general solution of the first-order linear partial differential equation xux + yuy =u it and investigate first-order, quasi-linear and linear partial differential equations. 

To transform + = — into a linear differential equation with constant coefficients, di2 dx x the required substitution is (a) x = sin t (b) x=t4+1 (c) x = log t (d) x = el 

Find the general solution of the first-order linear partial differential equation

xu_x yu_y = u and investigate first-order, quasi-linear and linear partial differential equations

Obtain PDE z = x + ax² y² where a and b are arbitrary constants and also

analyze the partial differential equation. 

(y+z)p+(z+x)q =x+y