Differential Equations Answers

Reduce the following PDEs to a set of three ODEs by method of separation of variables 1/R(d/Dr(rdv/dv))+1/r(d

Solve the following ODE using the power series method:
(x + 2)y" + xy' − y = 0

P2+ 2 py cot x=y2

solve (2x+3)^2d^2y/dx^2-(2x+3)dy/dx-12y=6x

(2x+1)^2 d^2y/dx^2 - 2(2x+1) dy/dx- 12y= 6x
solve by taking substitution (2x+1)= e^t

y dy+x dx = √x^2+y^2dx

Using the method of undermined coefficient find the general solution of D.E
y^iv-2y^'''+2y^''=3ye^-x+2e^-x(x)+e^-xsinx.

Verified that the equations
1.z=root(
2x+a)+root(2y+b) and
2.z^2+meu=2(1+lemda^-1)(x+lemda y)

are both complete integrals of the PDE z=1/p+1/q.Also show that the complete integral (2)is the envelope of the one parameter sub-system obtained by taking b=-a/lemda-meu/(1+lemda) in the solution (1)

Solve the PDE
1.(D^2+D-1)z=4e^(x+y) cos(x+y)
2.(D+D'-1)(D+2D'-3)z=4+3x+6y

Solve the equation
x dy/dx−ay=x+1
, where a is a constant

a. y=x/1−a − 1/a+cx
b. y=x/1−a + 1/a+cx
c. y=x/1+a − 1/a+cx
d. y=−x/1−a − 1/a+cx