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Popular Calculus >

x^3y^'+x^2y=x^7y^{3/4}

Solution

x^{3} y^{^{'}} + x^{2} y = x^{7} y^{\frac{3}{4}}

Solution

y = \frac{x ^{20}}{194481} + \frac{4 c _{1} x ^{\frac{59}{4}}}{9261} + \frac{2 c _{1}^{2} x ^{\frac{19}{2}}}{147} + \frac{4 c _{1}^{3} x ^{\frac{17}{4}}}{21} + \frac{c _{1}^{4}}{x}

Solution steps

x^{3} y^{'} (x) + x^{2} y = x^{7} y^{\frac{3}{4}}

Solve Bernoulli ODE:

y = \frac{x ^{20}}{194481} + \frac{4 c _{1} x ^{\frac{59}{4}}}{9261} + \frac{2 c _{1}^{2} x ^{\frac{19}{2}}}{147} + \frac{4 c _{1}^{3} x ^{\frac{17}{4}}}{21} + \frac{c _{1}^{4}}{x}

y = \frac{x ^{20}}{194481} + \frac{4 c _{1} x ^{\frac{59}{4}}}{9261} + \frac{2 c _{1}^{2} x ^{\frac{19}{2}}}{147} + \frac{4 c _{1}^{3} x ^{\frac{17}{4}}}{21} + \frac{c _{1}^{4}}{x}

Graph

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Frequently Asked Questions (FAQ)

What is the solution for x^3y^'+x^2y=x^7y^{3/4} ?
The solution for x^3y^'+x^2y=x^7y^{3/4} is