Ejercicios de repaso sección 2.6

Resolver las ecuaciones diferenciales de Bernoulli.

  1. dydx−y=exy2\hspace{0.5cm}\dfrac{dy}{dx}-y=e^xy^2

  2. xdydx−(1+x)y=xy2\hspace{0.5cm}x\dfrac{dy}{dx}-(1+x)y=xy^2

  3. xdydx+y=1y2\hspace{0.5cm}x\dfrac{dy}{dx}+y=\dfrac{1}{y^2}

  4. 3(1+t2)dydt=2ty(y3−1)\hspace{0.5cm}3(1+t^2)\dfrac{dy}{dt}=2ty(y^3-1)

  5. y12dydx+y32=1\hspace{0.5cm}y^{\frac{1}{2}}\dfrac{dy}{dx}+y^{\frac{3}{2}}=1                Sujeta a y(0)=4y(0)=4

  6. x2y′+2xy−y3=0\hspace{0.5cm}x^2y^{'}+2xy-y^3=0

  7. dydx−y=xy5\hspace{0.5cm}\dfrac{dy}{dx}-y=xy^5

  8. y′−(1+1x)y=y2\hspace{0.5cm}y^{'}-\left( 1+\dfrac {1}{x}\right) y=y^{2}

  9. y′+1xy=23x4y4\hspace{0.5cm}y^{'}+\dfrac{1}{x}y=\dfrac{2}{3}x^4y^{4}

  10. dydx−2xy=3x2y4\hspace{0.5cm}\dfrac{dy}{dx}-\dfrac{2}{x}y=\dfrac{3}{x^2}y^4