Final answer to the problem
$\frac{e^{3x}}{y^{3}}=-3\left(\frac{1}{3}x^3e^{3x}-\frac{1}{3}x^{2}e^{3x}+\frac{2}{9}xe^{3x}-\frac{2}{27}e^{3x}\right)+C_0$
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Step-by-step Solution
Specify the solving method
1
Rewrite the differential equation using Leibniz notation
$\frac{dy}{dx}-y=x^3y^4$
Learn how to solve differential equations problems step by step online.
$\frac{dy}{dx}-y=x^3y^4$
Learn how to solve differential equations problems step by step online. Solve the differential equation y^'-y=x^3y^4. Rewrite the differential equation using Leibniz notation. We identify that the differential equation \frac{dy}{dx}-y=x^3y^4 is a Bernoulli differential equation since it's of the form \frac{dy}{dx}+P(x)y=Q(x)y^n, where n is any real number different from 0 and 1. To solve this equation, we can apply the following substitution. Let's define a new variable u and set it equal to. Plug in the value of n, which equals 4. Simplify.
Final answer to the problem
$\frac{e^{3x}}{y^{3}}=-3\left(\frac{1}{3}x^3e^{3x}-\frac{1}{3}x^{2}e^{3x}+\frac{2}{9}xe^{3x}-\frac{2}{27}e^{3x}\right)+C_0$