(dy)/(dt)=t^2y+1+y+t^2

Lösung

\frac{d y}{d t} = t^{2} y + 1 + y + t^{2}

y = e^{\frac{t ^{3}}{3} + t + c_{1}} - 1

Schritte zur Lösung

\frac{d y}{d t} = t^{2} y + 1 + y + t^{2}

Solve separable ODE:

y = e^{\frac{t ^{3}}{3} + t + c_{1}} - 1

y = e^{\frac{t ^{3}}{3} + t + c_{1}} - 1

e^{x + y} y^{^{'}} = x, y (0) = ln (2)

y^{^{'}} = y + 5

(x ln (x^{2})) y^{^{'}} = 2 y

\frac{d y}{d t} + 0.5 t y = 4 t

\frac{d y}{d x} = \frac{y ^{2}}{x}, y (e) = 3