Differential Equations Answers

solve the D.E. ydouble prime =1+( y prime)^2

Apply the method of variations of parameters to solve the following differential equations:
a) x^2y double prime+xyprime-y=x^2e^x

particle moves in a circle according to the equation \\(\\bar{r}=cos (t^2)\\hat{i} +sin(t^2)\\hat{j}\\). The magnitude of the normal component of the acceleration at time \\(t\\) is

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