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First order differential equations Calculator

Get detailed solutions to your math problems with our First order differential equations step by step calculator. Sharpen your math skills and learn step by step with our math solver. Check out more online calculators here.

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Solved example of First order differential equations

$\frac{dy}{dx}=x^2y$
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Multiply both sides of the equation by $dx$

$dy=x^2ydx$
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Integrate both sides, the left side with respect to $y$, and the right side with respect to $x$

$\int1dy=\int x^2dx$
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The integral of a constant is equal to the constant times the integral's variable

$y=\int x^2dx$
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Apply the power rule for integration, $\displaystyle\int x^n dx=\frac{x^{n+1}}{n+1}$, where $n$ represents a constant function

$y=\frac{x^{3}}{3}$
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Simplifying the fraction

$y=\frac{1}{3}x^{3}$
7

As the integral that we are solving is an indefinite integral, when we finish we must add the constant of integration

$y=\frac{1}{3}x^{3}+C_0$

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