Differential Equations Answers

Show that y= c₁e^x + c₂e^2x is the general solution of y’’-3y’+2y=0 on any interval, and find the particular solution for which y(0)=-1 and y’(0)=1

show that y=c1e^x+c2e^2x is the general solution of y''-3y'+2y=0 on any interval, and find the particular solution for which y(0)=-1 and y'(0)=1

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.