- #1
Physics345
- 250
- 23
- Homework Statement
- y(x+y+1)dx+(x+2y)dy=0
- Relevant Equations
- (My-Nx)/n
dM/dY = x+2y+1 dN/dx = 1
(My-Nx)/n = 1 Integrating Factor => e^∫1dx= e^x
(xye^x+ye^x+ye^x)dx + (xe^x+2ye^x)dy = 0
dM/dY =xye^x+e^x+2ye^x dN/dx = xye^x+e^x+2ye^x Exact
∫dF/dy * dy = ∫ (xe^x+2ye^x)dy
F = xy*e^x + y^2*e^x + c(x)
dF/dx = xy*e^x + y*e^x + y^2 * e^x + c'(x)
c'(x) = 0
c(x) = c
Therefore, the general solution to the ODE is xye^x + y^2 * e^x + c = 0
Did I miss something here? The doubt stems from c'(x) = 0
Is there any way I can confirm the answers to my ODE solutions?
Thanks for the help everyone.
(My-Nx)/n = 1 Integrating Factor => e^∫1dx= e^x
(xye^x+ye^x+ye^x)dx + (xe^x+2ye^x)dy = 0
dM/dY =xye^x+e^x+2ye^x dN/dx = xye^x+e^x+2ye^x Exact
∫dF/dy * dy = ∫ (xe^x+2ye^x)dy
F = xy*e^x + y^2*e^x + c(x)
dF/dx = xy*e^x + y*e^x + y^2 * e^x + c'(x)
c'(x) = 0
c(x) = c
Therefore, the general solution to the ODE is xye^x + y^2 * e^x + c = 0
Did I miss something here? The doubt stems from c'(x) = 0
Is there any way I can confirm the answers to my ODE solutions?
Thanks for the help everyone.