Ejercicios de repaso sección 2.3

Determinar si la E.D. es exacta, si lo es revuélvala.

  1. (2x+4)dx+(3y−1)dy=0\hspace{0.5cm}(2x+4)dx+(3y-1)dy=0

  2. (2x+y)dx+(x+6y)dy=0\hspace{0.5cm}(2x+y)dx+(x+6y)dy=0

  3. (x+y)(x−y)dx+x(x−2y)dy=0\hspace{0.5cm}(x+y)(x-y)dx+x(x-2y)dy=0

  4. xdydx=2xex−y+6x2\hspace{0.5cm}x\dfrac{dy}{dx}=2xe^x-y+6x^2

  5. (2y−1x+cos⁡3x)dydx+yx2−4x3+3ysen3x=0\hspace{0.5cm}\left( 2y-\dfrac {1}{x}+\cos 3x\right) \dfrac {dy}{dx}+\dfrac {y}{x^{2}}-4x^{3}+3ysen3x=0

  6. (x+y)2dx+(2xy+x2−1)dy=0\hspace{0.5cm}(x+y)^2dx+(2xy+x^2-1)dy=0           Sujeta a y(1)=1y(1)=1

  7. (4xy3+3y2+1)dx+(6x2y2+6xy)dy=0\hspace{0.5cm}(4xy^3+3y^2+1)dx+(6x^2y^2+6xy)dy=0

  8. (2x−1)dx+(3y+7)dy=0\hspace{0.5cm}(2x-1)dx+(3y+7)dy=0

  9. (x+2y)dx+(x+2y)dy=0\hspace{0.5cm}(x+2y)dx+(x+2y)dy=0

  10. (yln⁡∣y∣−e−xy)dx+(1y+xln⁡∣y∣)dy=0\hspace{0.5cm}\left( y\ln \left| y\right| -e^{-xy}\right) dx+\left( \dfrac {1}{y}+x\ln \left| y\right| \right) dy=0