Question

how to solve exact equation (3x^2y+e^y)dx + (x^3+xe^y-2y)dy=0
when x=0 and y=1

Answer 1

can i give you general method?

Answer 2

yes @niksva

Answer 3

Mdx + Ndy = 0
is said to be an exact differential equation if it satisfies the following condition
\[\frac{ dM }{ dy } = \frac{ dN }{ dx }\]
where dM/dy = differential coefficient of M w.r.t y keeping x constant
and dN/dy = differential coefficient of N w.r.t x keeping y constant

Answer 4

method to solve is given in the steps
1) Integrate M w.r.t x keeping y constant
2) Integrate w.r.t y , only those terms of N which do not contain x
3) result of 1) + result of 2) = constant

Answer 5

lastly use the boundary conditions to solve for constant

Answer 6

like this?
\[M=3^{2}y+e ^{y}
N=x ^{3}+xe ^{y}-2y\]

Answer 7

yeah it is
hope u can solve now
if u get any problem is solving further , feel free to ask me

Answer 8

*in