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Solve the following differential equation by using separation of variables method: dp/dt =(1+p^2)cos(t)/psin(t)


Solve the differential equation d2y
/dx2 + 2dy/dx + 4y = 111e2x cos3x
using the method of undermined coefficients.
Solve (D2 + a2)y = sinax

Solve (x + 2)y"-(2x + 5)y'

+ 2y = (x + 1)ex


dr/dΩ+rTanΩ=cos2Ω

dr/dΩ+tanΩ=cos2Ω


Find the nature and critical point of the system
dx/dt = (x)^2 +3xy+2(y)^2 and
dy/dt= 4-(x)^2

Write the three dimensional heat equation of partial differential equation.


Equation 𝑓(𝑧, 𝑝, 𝑞) = 0 , it’s solution is given by


 Eliminate 𝑎, 𝑏 and 𝑐 from 𝑧 = 𝑎(𝑥 + 𝑦) + 𝑏(𝑥 + 𝑦) + 𝑎𝑏𝑡 + 𝑐.