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Popular >

x(dy)/(dx)+2y=x^2

Solution

x \frac{d y}{d x} + 2 y = x^{2}

Solution

y = \frac{x ^{2}}{4} + \frac{c _{1}}{x ^{2}}

Solution steps

x \frac{d y}{d x} + 2 y = x^{2}

Solve linear ODE:

y = \frac{x ^{2}}{4} + \frac{c _{1}}{x ^{2}}

y = \frac{x ^{2}}{4} + \frac{c _{1}}{x ^{2}}

Popular Examples

limit as x approaches 0 of x/(sin^2(x))

x \to 0 lim (\frac{x}{sin ^{2} ( x )})

derivative of x/(8x+3)

\frac{d}{d x} (\frac{x}{8 x + 3})

(dy)/(dx)=(3-2y)*x^3

\frac{d y}{d x} = (3 - 2 y) \cdot x^{3}

integral of (ln(x))/(x(1+ln^2(x)))

\int \frac{ln ( x )}{x ( 1 + ln ^{2} ( x ) )} d x

integral from 0 to 15 of 1000e^{-0.05x}

\int_{0}^{15} 1000 e^{- 0.05 x} d x

Frequently Asked Questions (FAQ)

What is the solution for x(dy)/(dx)+2y=x^2 ?
The solution for x(dy)/(dx)+2y=x^2 is y=(x^2)/4+(c_{1})/(x^2)