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Popular >

y^'=sqrt(y),y(1)=1

Solution

y^{^{'}} = y, y (1) = 1

Solution

y = \frac{t ^{2}}{4} + \frac{t}{2} + \frac{1}{4}

Solution steps

y^{'} (t) = y

Solve separable ODE:

y = \frac{t ^{2}}{4} + \frac{t}{2} + \frac{1}{4}

y = \frac{t ^{2}}{4} + \frac{t}{2} + \frac{1}{4}

Popular Examples

integral of x/(sqrt(1-x^2))

\int \frac{x}{1 - x ^{2}} d x

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\frac{d}{d x} (arccos (4 x))

(\partial)/(\partial y)(ln|x+y|)

\frac{\partial}{\partial y} (ln ∣ x + y ∣)

(dy)/(dx)=e^{3y+10x}

\frac{d y}{d x} = e^{3 y + 10 x}

derivative of sin(x(1-cos(x)))

\frac{d}{d x} (sin (x) (1 - cos (x)))

Frequently Asked Questions (FAQ)

What is the solution for y^'=sqrt(y),y(1)=1 ?
The solution for y^'=sqrt(y),y(1)=1 is y=(t^2)/4+t/2+1/4