Differential Equations Answers

: 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

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?

Find the area of the parallelogram with sides a=i-2j+k and b=2i+j+k

Solve the differential equation (1 + yx) xdy + (1 − yx) ydx = 0

Q. Obtain the partial differential equation by eleminating the arbitrary constant from the relation
u=aeby+sinbx

Q. Obtain the partial differential equation by eleminating the arbitrary constant from the relation
u=xy+y√(x^2-a^2 )+b