Differential Equations Answers

form the differential equation for this
y=ae^x+bln|y|+c+d

find the solution of separable ODE
dy+x^2dx=x^2e^ydx

find solution of separable ODE
3e^xtanydx+(1-e^x)sec^ydy=0

Solve y"-5y'-6y=e^(-2t) where y’(0) = 1 and y(0) = -1 using LaPlace Transforms

find the solution of :-
x'(t)= -1/2 *x(t)+2x(t-1)e^(-5x(t-1))
where x(t)=1 , t belongs to [-1,0]

(b) Locate the critical points and determine their nature for the function

f(x)=-2x2+1/4x2

Identify the typesof differential equation, such linear/nonlinear, homogeneous/nonhomogeneous
Solve the initial value problem
Determine the interval of exsistence, if you can find an explicit solution

y' + 2ty = 4t, y(0) = -4

dy/dt + 1/t*y = ty^2

y' = -y +ty^-2, y(0) = 2

(2y - siny)y' + t =sint, y(0) = 0

Determine whether the given differential equation is exact. If it is exact, solve it.
(5x+4y) dx + (4x-8y^3) dy =0.

how to differentiate x = L sin Ɵ/2 + L/2 sin Ɵ/2