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Solve the Bernoulli Equation "xyy'+y^2=2x"
Use appropriate substitution to reduce the following equation to a variable separable and then solve the given IVP: "dy\/dx= (3x+2y)\/(3x+2y+2), y(-1)=-1"
Show that the coefficients of the given differential equation are homogeneous and solve the given differential equation: "-ydx+(x+\u221axy)dy=0"
(d^2-5d+6)y =x cos(2x)
1. y²dx-(xy+y²)dy=0
Let substitution v=y/x ; y=vx ; dy= vdx+xdv
2. x²dy+(2xy-y²)dx=0
Let substitution v=y/x ; y=vx ; dy= vdx+xdv
Determine the form of a particular solution for each differential equation. No need to solve for the general solution of the differential equation.
1. y'' − 3y' + 2y = xe^x + 1
Find the integral surface of the PDE:
x²p + y²q +z² =0
which passes through the hyperbola
xy =x+y, z=1.
Solve (p + q)(px + qy) = 1, using Charpit’s method.
Solve:
x².d²y/dx² -x.dy/dx +y=ln x
(D^4 +13D^2 + 36)y = 0
