Differential Equations Answers

 Find the general solution of the equation y^''− 4y^'+ 13y = 0.

 Find the general solution of the equation y^''− 4y^'+ 4y = 0. 

Solve the equation (dy/dx) − y = e^xy²

 Determine if the differential equation (sin y − y sin x)dx + (cos x + x cos y − y)dy = 0 is exact. If it is exact, solve it.

Use the integrating factor to solve the differential equation. dz/dy = z tan y + sin y

Obtain the partial differential equation by eliminating the arbitrary constant from the relation

x^2/a^2 +y^2/b^2 +u^2/c^2 =1

(e^2x + 4) dy/dx = y

state and prove the necessary conditions for the existence of maximum value and minimum value?

Solve the following initial value problem

Ut(x,t)=10Uxx(x,t) -10

U(-1,t)=U(1,t) Ux(-1,t)=Ux(1,t) t>0

Ux(x,0)=x+1 -1