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Find the general solution of the given differential equation

dr / d theta + rsec theta = cos theta
Solve
L^-1 × ((s^2 - 5s - 7)/(s + 2)^3)
Find the particular integral of
(x-1)^2 y" - 2(x-1)y' + 2y = (x-1)^2 y(0) = 3, y'(0) = 6
Solve the differential equation
y" + 4y' + 4y = 2cos2x + e^-x, y(0) = -1, y'(0) = 2
Solve the following differential equations cosx d²y/dx²+sinx dy/dx - 2ycos³x = 2cos^5 x

2z=(ax+y)^2+b


d²V/dt² -4V = 8e^(2t)

When t=0 and V=4 and dV/dt = 6


What is the generation time (min) of 102 E. Coli cell (CFU/g) growing logarithmically for 6 h produce 1.7 x 106 CFU/g?
Solve the given differential equation using an appropriate substitution. The DE is a bernoulli equation.

t^2 dy/dt + y^2 = ty
1. Solve the given differential equation using an appropriate substitution. The DE is a Bernoulli equation,

dy/dx = y(xy^6 - 1)

2. Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli equation.

x dy/dx + y = 1/y^2
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