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Popular >

f^'(x)=f(x)

Solution

f^{^{'}} (x) = f (x)

Solution

f (x) = e^{x + c_{1}}

Solution steps

f^{'} (x) = f (x)

Solve separable ODE:

f (x) = e^{x + c_{1}}

f (x) = e^{x + c_{1}}

Popular Examples

y^{^{'}} = \frac{1 + x}{y}

sin(2x)dx+cos(9y)dy=0,y(pi/2)= pi/9

sin (2 x) d x + cos (9 y) d y = 0, y (\frac{π}{2}) = \frac{π}{9}

(dy)/(dx)=(9+y^2)(3+x^2)

\frac{d y}{d x} = (9 + y^{2}) (3 + x^{2})

y^{^{'}} = 3 y^{2} - 3 y

x^3y^'-(8x^2-5)y=0,y(1)=2

x^{3} y^{^{'}} - (8 x^{2} - 5) y = 0, y (1) = 2

Frequently Asked Questions (FAQ)

What is the solution for f^'(x)=f(x) ?
The solution for f^'(x)=f(x) is f(x)=e^{x+c_{1}}