Differential Equations Answers

find a series solution in powers of x of the equation

2x²d²y/dx²+xdy/dx+(x²-1)y=0

find the general solutions for each of the following

1. (3x²+9xy+5y²)dx-(6x²+4xy)dy =0 y(2)=-6
2. x²dy/dx +xy=y³/x

solve

1.d²y/dx²-2dy/dx+5y=e^xtan2x

2.dy/dx+3y=3x²e^-3x

1. solve each of the following

a) (6xy+2y²-5)dx +(3x²+4xy-6)dy=0 y(1)=2

b)x²d²y/dx²+xdy/dx+4y=2xlnx

solve 2xydy+(3x^2+4xy)dx=0

A particle starts at the origin and moves along the positive x-axes such that its distance from the origin at any time is determined by the equation: x=2t^3 -9t^2 +12t Find the 3.1) times when the velocity is zero. 3.2) acceleration when the velocity is zero.

Solve the equations by the use of the operator D

D²y -6Dy +9y= e^3x + e^-3x

Suppose y₁ and y₂ are two solutions of the equation t²y^''+2t²y^'-t^-2y=0. Find W(y₁.y₂)(t).

Equation y''- y= 0 has a solution y= C₁e^t

1.solve the following differential equation by using separation of variables method:

1.1.x(dy/dx)=4y.

2.show whether or not the following differential equations are separable:

2.1.dy/dx=t(in(s^2t))+8t².

2.2.dy/dx=ye^x+y/x²+2.

2.3.dy/dx=x+1/y-1.