Differential Equations Answers

Solve the partial differential equation

Px+q=p^2

Xyp+y^2q+2x-xyz

Solve (2𝑥 + 𝑡𝑎𝑛𝑦)𝑑𝑥 + (𝑥 − 𝑥

2

𝑡𝑎𝑛𝑦)𝑑𝑦 = 0

Determine the general solution to the equation ∂²u/∂t²=c²(∂²u/∂x²) under the boundary conditions u(0,t)=u(1,t)=0 and initial conditions u(x,0)=Φ(x), u_t(x,o)=Ψ(x)

Solve: z(x+2y)p-z(2x+y)q=y^2-x^2

Reduce each of the following equations into canonical form and find the general solution: (a) Uz + xy = u, (b) ux + x +y = y, (C) ux + 2xy uy = x, (d) Uz – yuy – u = 1.

Solve: z(x+2y)p-z(2x+y)q=y^2-x^2

Solve( D^2+ DD'-6D'^2)z= cos(2x+y)

Prove that y(x) = C1 sin2x + C2 cos2x is a solution of y

(2) + 4y = 0

At a particular point of curve y=2x² -x +q, the equation of tangent is y= 3x-5, Find the.value of the constant q