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Differential equations Calculator

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1

Solved example of differential equations

$\frac{dy}{dx}=\sin\left(5x\right)$
2

Multiply both sides of the equation by $dx$

$dy=\sin\left(5x\right)dx$
3

Integrate both sides, the left side with respect to $y$, and the right side with respect to $x$

$\int1dy=\int\sin\left(5x\right)dx$
4

The integral of a constant is equal to the constant times the integral's variable

$y=\int\sin\left(5x\right)dx$
5

Apply the formula: $\int\sin\left(ax\right)dx$$=-\left(\frac{1}{a}\right)\cos\left(ax\right)$, where $a=5$

$y=-\frac{1}{5}\cos\left(5x\right)$
6

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

$y=-\frac{1}{5}\cos\left(5x\right)+C_0$

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