Differential Equations Answers

Find the particular solution of the initial value problem

d²y/dx² + 4 dy/dx + 13y = 0

y(0)=1

y¹(0)=4

Show that the following equation is exact

( x² + y²) dx + 2xydy = 0

Solve the differential equation

dy/dx=- 2xy²

find the value of n for which the equations (n-1)^2 Uxx - y^2n Uyy= ny^2n-1 is parabola and hyperbola

solve the differential equation dy/dx + (x/1-x^2)y = x(y)^1/2 , y(0)=1

given that y(x) =x^-1is one solution of the differential equation 2 x^2 y ′′ +3x y' − y = 0 x>0 find a second linearly independent solution of the equation

solve the differential equation dy/dx(x/1-x^2)y=xy^1/2 , y(0)=1

Find the partial differential equation arising from f[z/x^3,y/z]=0, where f is an arbitrary function of the arguments. Also find the general solution of the PDE obtained.

Given that z = ax +sqrt (a^2 − 4y) + c is the complete integral of the PDE, p^2 − q^2 =4 determine its general integral.

Find the values of n for which the equation (n-1)²uxx - y^2n uyy = ny^(2n-1)uy is

i) parabolic ii) hyperbolic.