Differential Equations Answers

Calculate the surface integral, F.ds, where F = 2(x,y,z), and where S is the surface of the cube define by the relations 0≤x≤1, 0≤y≤1, 0≤z≤1.

Solve the following differential equations
(i) x^2 p + y^2 q = ( x+ y) z .
(ii) (root of p) − (root of q) + 3x = 0

Find the equation of the integral surface of the differential equation
(x^2 − yz) p + ( y^2 − zx) q = z^2 − xy
which passes through the line x =1, y = 0

Solve the following differential equations
(i) [D^3 − DD′^2 − D^2 + DD′] z = 0
(ii) [D^4 − D′^4 − 2D^2 D′^2 ] z = 0 .
(iii) [D^2 − 2DD′ + D′^2 ] z =12xy

Q. solve (D4+8D2−9)y=9x3+5cos2x

Q. solve (D3−7D+12)y=x3−5x2

Q. solve (D3−7D−6)y=1+x

Q. Solve the following differential equation:
(D3−D2+3D+5)y=exsin2x

Q. Solve the following differential equation:
(D3+D2−4D+4)y=e2x

Q. Find an equation of orthogonal trajectory of the curve of each of the following:
(i) x=cy2
(ii) x2+y2=cx
(iii) y=ecx
(iv)xy=c
(v)y2=x2+cx