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Obtain the characteristic curves for the partial differential equation 4uxx+5uxy+uyy+ux+uy=0.
Reduce the PDE uxx+xuyy
into a canonical form in the region
x<0.
Solve the initial-value problem : (dx)/(dt) +(tant)x=cos^2(t), x(0)=-1
Initially 100 milligrams of a radioactive . After 6 hours the mass had decayed by 3% the rate of decay is proportional to the amount of substance present at time t amount remaining after 24 hours .
Initially milligrams of a radioactive . After hours the mass had decayed by the rate of decay is proportional to the amount of substance present at time amount remaining after hours .
The population of bacteria in a culture grows at a rate proportional to the number of bacteria present at time .After hours it is observed that there are After hours there are bacteria present. bacteria present. Find the initial number of bacteria .

Solve the following lengendre differential equation.

(1-x2)y"-2xy'+l(l+1)y=0


Using power series method,solve the following differential equation

(x3+3)y"+4xy'+y=0


  • A certain substance can cool itself from 110°C to 70°C in 15minutes. If the air’s temperature is 30°C, how long will it take to cool from 110°C to 50°C?

find the relation between D and Δ of following differential equation 4(2x+1)^2 d^2y/dy^2 -4(2x+1)dy/dx + 3y =ln(2x+1))


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