Chardonnay Felix

2021-09-21

Find the general solution of the differential equation or state that the differential equation is not separable.
${y}^{\prime }={x}^{6}y$

pivonie8

Step 1
Given differential equation:
${y}^{\prime }={x}^{6}y$
Convert the above differential equation in the first order separable ordinary differential equation
$\frac{{y}^{\prime }}{y}={x}^{6}$
Step 2
Integrate the both sides, we get
$\int \frac{dy}{y}=\int {x}^{6}dx$
We know that $\int {x}^{n}dx=\frac{{x}^{n+1}}{n+1}+c$
where, "c" is integrating constant.
$\mathrm{ln}\left(y\right)=\frac{{x}^{7}}{7}+c$
$y={e}^{\frac{{x}^{7}}{7}+c}$

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