Determine whether the given differential equation is exact. If it is exact. If it is exact, solve it. (If it is not exact, enter NOT) (x^2 - y^6 )dx + (x^2 - 6xy)dy = 0
Determine whether the given differential equation is exact. If it is exact. If it is exact, solve it. (If it is not exact, enter NOT) (1 + ln?(x) + y/x)dx = (4 - ln?(x))dy
Determine whether the given differential equation is exact. If it is exact. If it is exact, solve it. (If it is not exact, enter NOT) (x - y^5 + y^2 sin?(x))dx = (5xy^4 + 2ycos?(x))dy
Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. xdx + (y - 2x)dy = 0
Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. dy/dx = y-x/y+x
Solve the given differential equation by using an appropriate substitution. The DE is homogeneous. x dy/dx = y + sqrt(x^2 - y^2 ), x > 0
Solve the given initial value problem. The DE is homogeneous. xy^2 dy/dx = y^3 - x^3, y(1) = 2
Solve the given initial value problem. The DE is homogeneous. (x + ye^(y/x) )dx - xe^(y/x) dy = 0 , y(1) = 0
The population of a community is known to increase at a rate proportional to the number of people present at time t. If an initial population P0 has doubled in 3 years, how long will it take to triple? How long will it take to quadruple? (Round your answer to 1 decimal place.)
The population of a town grows at a rate proportional to the population present at time t. The initial population of 500 increases by 20% in 10 years. What will be the population in 60 years? (Round your answer to the nearest person) How fast (in persons/year) is the population growing at t=60? (Round your answer to two decimal places)