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Thepotemich [5.8K]
3 years ago
13

Solve x'=5t(sqrt(x)) x(0)=1

Mathematics
1 answer:
LekaFEV [45]3 years ago
8 0

Answer:

2\sqrt{x}=\frac{5t^2}{2}+2

Step-by-step explanation:

Given: \frac{\mathrm{d} x}{\mathrm{d} t}=5t\sqrt{x}\,,\, x(0)=1

Solution:

A differential equation is said to be separable if it can be written separately as  functions of two variables.

Given equation is separable.

We can write this equation as follows:

\frac{dx}{\sqrt{x}}=5t\,dt

On integrating both sides, we get

\int \frac{dx}{\sqrt{x}}=\int 5t\,dt

Formulae Used:

\int \frac{1}{\sqrt{x}}=2\sqrt{x}\,\,,\,\,\int t\,dt=\frac{t^2}{2}

So, we get solution as 2\sqrt{x}=\frac{5t^2}{2}+C

Applying condition: x(0) = 1, we get C=2

Therefore, 2\sqrt{x}=\frac{5t^2}{2}+2

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