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شائع >

(dy)/(dx)=4(y^2+1),x(pi/4)=1

الحلّ

\frac{d y}{d x} = 4 (y^{2} + 1), x (\frac{π}{4}) = 1

الحلّ

y = tan (4 x + c_{1})

خطوات الحلّ

\frac{d y}{d x} = 4 (y^{2} + 1)

Solve separable ODE:

y = tan (4 x + c_{1})

y = tan (4 x + c_{1})

أمثلة شائعة

2x(dy)/(dx)=(2x+1)y

2 x \frac{d y}{d x} = (2 x + 1) y

(dx)/(dt)=-(sqrt(x))/(50pi)

\frac{d x}{d t} = - \frac{x}{50 π}

(dy)/(dx)=((x+2))/((2y))

\frac{d y}{d x} = \frac{( x + 2 )}{( 2 y )}

x^2(dy)/(dx)+xy=3x

x^{2} \frac{d y}{d x} + x y = 3 x

y^'=(5sin(x))/(sin(y)),y(0)= pi/2

y^{^{'}} = \frac{5 sin ( x )}{sin ( y )}, y (0) = \frac{π}{2}