Differential Equations Answers

Find the general solution of y′+2y=x3e−2x

If y=2x+Cex is a solution of the differential equationdydx−y=2(1−x) then find the particular solution satified by x=0, y=3

: Find the general solution of y′−2xy=1

Suppose
y
=
2
e
−
4
x
y=2e−4x
is the solution to the initial value problem
y
′
+
k
y
=
0
,
y
(
0
)
=
y
0
y′+ky=0,y(0)=y0
. Find the value of
y
0

Q. Solve thefollowing Inintial boundary value problem:
uxx=1/c^2 utt 0<x<L (t>0)
(B.C,s) u(0, t)=u(L, t)=0 ( t>0)
(I.C,s) u(x,0)=0
ut(x,0)=(∂y/∂x)t=0=g(x)

Q. Solve the following Inintial boundary value problem:
uxx=1/c^2 ut c<x<L (t>0)
(B.C,s) u(0, t)=u(L, t)=0
(I.C,s) u(x,0)=f(x)= x if 0<x<L/2, -x if L/2<x<L

Find the temperature in a bar of length l with both ends insulated and with initial
temperature in the rod being sin ( π x / l ) .
.

Solve the following differential equations
i) (x^2) p + (y^2) q = (x + y ) z
ii) √p - √q + 3x = 0

Solve, using the method of variation of parameters
(d2y/dx2) - y = 2/(1+e^​x)

dx/dy=(x^2-y^2)/2x is it a homogeneous differential equation?