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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
solve partial differential equations d²z/dx² + 2d²z/dxdy + d²z/dy² = 2 cos y - x sin y
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= C1et
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.
x^2d^2y/dx^2-xdy/dx+y=log x+sin(log x)+1/x
find the general solution of the differential equation using method of variation of parameters (x^2+1)m^2-(2xm/(x^2+1))+(2/(x^2+1)=6(x^2+1)^2
2(1+x2)y"+4xy'-4y=0
In the following problem use a suitable substitution to reduce the order of the given DE and then solve it
- y''=2y'
- y''+eyy'2=0
- y"+(1-1/y)y'2=0
