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Popular >

x(x^3+1)y^'+(2x^3-1)y=((x^3-2))/x

Solution

x (x^{3} + 1) y^{^{'}} + (2 x^{3} - 1) y = \frac{( x ^{3} - 2 )}{x}

Solution

y = \frac{x ^{2}}{x ^{3} + 1} + \frac{1}{x ( x ^{3} + 1 )} + \frac{c _{1} x}{x ^{3} + 1}

Solution steps

x (x^{3} + 1) y^{'} (x) + (2 x^{3} - 1) y = \frac{( x ^{3} - 2 )}{x}

Solve linear ODE:

y = \frac{x ^{2}}{x ^{3} + 1} + \frac{1}{x ( x ^{3} + 1 )} + \frac{c _{1} x}{x ^{3} + 1}

y = \frac{x ^{2}}{x ^{3} + 1} + \frac{1}{x ( x ^{3} + 1 )} + \frac{c _{1} x}{x ^{3} + 1}

Popular Examples

derivative of 3log_{10}(x)

\frac{d}{d x} (3 lo g_{10} (x))

(\partial)/(\partial x)(1/(2x+4y^2))

\frac{\partial}{\partial x} (\frac{1}{2 x + 4 y ^{2}})

integral from 0 to 3 of x^2sqrt(9-x^2)

\int_{0}^{3} x^{2} 9 - x^{2} d x

integral of 1/(t^2sqrt(256-t^2))

\int \frac{1}{t ^{2} 256 - t ^{2}} d t

sum from n=0 to infinity of ((nx)/6)^n

n = 0 \sum \infty (\frac{n x}{6})^{n}

Frequently Asked Questions (FAQ)

What is the solution for x(x^3+1)y^'+(2x^3-1)y=((x^3-2))/x ?
The solution for x(x^3+1)y^'+(2x^3-1)y=((x^3-2))/x is y=(x^2)/(x^3+1)+1/(x(x^3+1))+(c_{1}x)/(x^3+1)